Okay, what we're going to do now is delete that animation off of the Sun because as I'm sure you've noticed, it's wrong because all the planets wouldn't rotate in a solar system in a perfect line. That's nuts. So let's sort that right out. So to do that, make sure you're on frame one. The reason you need to be on frame one is because when we remove the animation, all the objects will stay where they are. So if we were on frame 40 and we remove the animation, the planets are just going to stay there, they're not going to go back to the start position. So let's make sure we do it properly. So we're on frame one. And then making sure you've got the Sun selected and you can see your keyframes. To get rid of the animation, we're going to click on edit and then we're going to go down to delete by type and the way to get rid of animation is to click on channels and you'll see all that animation is gone. When we press play, nothing happens.


Hi, I'm Carlos, I'm representing Moopis Team on Educational Solutions and I'm going to provide a quick update of the work done during this spring. Okay, this time we don't have any sexy demos like a platform, but I promise that we will do some sexy, super sexy demos for the next time. So, for the activity cars side, you can see we have working of the new radio drop-downs for ability and for groups mode for the teachers, so that is easy for the teachers to do this task without going to the setting page. Also we have completed the drop-down to show the rules for the completion for the teachers and we are working to edit these restrictions just in a simple form with only the completion part there. Next slide, please. Okay, here we can see we have been working, we are working on the student view to see all the completion rules for the student and also we have resolved a super key task to see how we can implement and move these subpanels in the actions menu. That's allowed to work in a new drop-down radio button for these submenus inside the action menu that is going to be in the next spring, I hope.


Hello friends, welcome back to another episode here on the channel. I hope you're all doing great and as always for anyone new to the channel, welcome. And my name is Lee, also known as Osiris. Today, we're going to be covering some news in regards to online tournaments, Players Cup, Ham and all things in between. So yesterday, we had a tweet out from the Play Pokémon account, the official Play Pokémon account over on Twitter, announcing that Players Cup 4 would be taking place and taking place very soon. Now, right now, we are still in the midst of Players Cup 3. That tournament is still being played out, so we don't know the results of that. But to have an announcement of Players Cup 4 already is very exciting news. It will be coming up in the very near future. So we'll go over all the details today about how you can participate, all the changes as well that have been made because there are some big updates to the tournament structure in general that I think it warranted a video today just to go through this and try and get some of you that haven't maybe played before a little bit more involved and give you the opportunity to take part in this tournament because it is a lot of fun. It's great to do, especially because of things that are going on in the world right now. We know that real life in events aren't taking place at the moment. Hopefully they will be back soon. But in the meantime, we have got the ability to take part in official tournaments, sanctioned tournaments that makes it very exciting. So as you can see, this tweet was thrown up 18 hours ago yesterday. The Play Pokémon Players Cup 4 is coming. Here we go. While the conclusion of PlayScope 3 still awaits, this addition to our digital tournament series will keep up the momentum.  So very exciting news. If we head over to the actual pokemon.com website with all the information and all these links, everything that I'm covering today will be down in the description. If you want to take a closer look yourself or just have a bit more in-depth read through things, but we'll try and cover as much as we can throughout this video. So kicks off with the fourth installment of the Pokemon Players Cup is an online tournament taking place from April through late July 2021. So quite a good chunk of time that this tournament will be running. Players from around the world will have the opportunity to prove their metal as Pokemon trainers battle against other trainers around the world to win a share of wait for it. Wait for it. A winner share of $45,000 in prizes. So the big news first is we've got some amazing prize support. The prize support for players Cup one, two and three was good, but there is drawbacks with that top four players only got prizing and they they got an amazing prize. They got a travel award to a future international championship. So an amazing prize, the prospect of traveling places like South America, Australia, US, you know, phenomenal in Europe, obviously for you, you people that aren't in Europe. But I mean, it was really kind of harsh on the players getting top eight, top 16, top 32.  I'm pleased it's been addressed because it gives players something to kind of work towards. Now, $45,000 is split over three different formats, VG, TCG and Polkin. We'll get into the details as you go through the video and perhaps more importantly, Bragg and Wrights, one of the top Pokemon trainers in the world. And that's what we all want, the Bragg and Wrights, isn't it? That's what it's all about. You know, anyway, we'll move on. The fourth Pokemon players couple feature three separate competitions as you already mentioned, Pokemon TCG, one for the video game players and we'll be bringing back Polkin DX tournament as well, which is amazing news for those Polkin players out there. So three tournaments running consecutively, which is incredible. The video game competition will use Pokemon video game championship rules. So we'll get into that as we go through participation in the Pokemon players Cup four is limited to Masters Division players only.  It's unfortunate. It's something that's not being able to be, I guess, you know, it's a big tournament and to kind of facilitate every age division across every kind of platform that we've got. It's probably just too big an ask. So it is unfortunate. Hopefully that gets addressed in future, but you know, we're getting improvements each players Cup. So you've got to think in the future that might be a thing that happens. And like I say, real life events are coming back soon. Fingers crossed. So that will be not really an issue, will it? But it is only for Masters at this present time across all these different platforms. And the players Cup four will take place in three phases. So we'll have an open qualifier, a regional qualifier round and a global finals round. Be sure to check out the respected Pokemon TCG event, the video game event and poke and the event pages for information, including scheduling, pricing and more. The players who come out on top of the qualifier stages will be eligible to compete in the final stage of the Pokemon players Cup for in July. So that's when the global finals will be taken place. We'll get into the dates in a minute. Matches will be broadcast on the official Pokemon Twitch and YouTube channels. Very exciting. The streams are always very entertaining. Obviously, we're doing place Cup three right now as it's going on. So it's a very exciting time. And hopefully you guys catching that will enjoy all the action from players Cup three. Make sure to check out the respected Twitch and YouTube channels where they'll be broadcast and obviously they're going to be broadcasting this one, which is it? You know, we want we want that as spectator as we want that to be broadcast so we can see all these top players performing at the peak of their game and battling it out to be that number one trainer. You can learn more about the stream information from the stream information page. And I'm sure that will be updated soon with place Cup four because as I say, place Cup three is still ongoing qualifying for the players Cup for global finals. So here we go. Getting into the meat and bones of it from the players Cup for regional qualifiers. The following number of players will be selected to compete in the finals. So we'll skip trading card and polka and because we're going to concentrate a little bit more on the VG because that's predominantly what we do here on the channel, but they're pretty much the same across the board excluding polka. But like I say, all the information is going to be linked down below. So for the VG side of it, four players from each region will progress to the global finals. You're going to have four players from the US, four players from Europe, four players from Latin America and four players from Oceana. So very exciting. So it'll be 16 players in total going to the grand finals and then we'll get down to the pricing. So pricing for VG first place is going to get $5,000 nice very nice very nice. Then as you can see, it increments down second place 3,500 third place, 2,500 fourth place, 2,000 fifth place and I imagine this is fifth to fifth and sixth get 1,250 seventh eighth get 750 ninth to 13th or ninth 12th get 500 and then 13th I would imagine down to 16th will get $250. So very good. I mean amazing that you're going to be able to get these prizes. The only thing I would like to say is what I would love to see is and I'm sure it can be done. The prizes are amazing. I'm not complaining, but I've had conversation with a very close friend of mine about this, you know, you want a trophy. If you do well, you want a trophy. You want something to be able to keep. I would love to see them integrate a trophy into this, you know, if it's just for top four, just to have a trophy sent to you, you know, take some money off the pricing. I'm sure every player competing would say, take some of my prize money back and give me a trophy as well as the prize money. You know, it's just that commemorative kind of something physical to keep to put on display to show an achievement there. And that's that would be my only thing. This is an amazing step forward. But Pokemon tournaments have always had trophies always had trophies. Um, so, you know, people love putting them on display, putting the bricks on display, putting the nice trophies on display. That would be something personally I would like to see brought in anyway. They're the pricing so eligible players who qualify for the regional qualifiers for the Pokemon TCC of video game competition and also have a Pokemon TCC online account will receive a special in-game deck box and card sleeves. So there's, there's, it looks like we're getting freebies. I don't know, does it? Players must have logged into their Pokemon TCC online account with participating Pokemon Trainer Club account at least once prior to the start of the regional qualifiers in order to receive these items. They will not be rector, rector, uh, react. Um, I can't even read. I can't read. I do have issues. Granted, if players do not complete this step, it's on the page if you want to read it. Okay. Good luck in the Pokemon players. So it looks like eligible players who qualify in the region finals for Pokemon TCC video game competition or global finals for Pokemon DX and also have a Pokemon online account will receive a special in-game deck box. So all everyone that qualifies for the, um, for the regional qualifiers, excluding Pokemon day, Pokemon DX get a regional deck box. So make sure that you've got your, your details updated on the Pokemon, uh, your account page. Right. Now let's get over to meeting bones of this for the video game because that's what we're going to be concentrating on today. Uh, this is the VG page again. It'll be linked down in the description below. Master's division Pokemon trainers competing in the fourth Pokemon players cup for Pokemon sword and Pokemon shield will battle through several tournament phases, battles in each phase will adhere to current Pokemon world championship, uh, rules. So going into the qualifiers will be in series eight because the qualifiers are going to run from I think the ninth of April like it states here till the 11th of April. So that is still going to be series eight one restricted Pokemon current rule set right now. Then we're going to be moving into series nine, which from all accounts I understand it's going to be reverting back to series seven rules, but let's not make assumptions until we've got a fully confirmed announcement on what will be taking place for players cup. You would imagine it'll be series seven for the regional qualifiers and global finals, but we don't know. We don't know until there's that confirmation, but they are going to follow the current video game championship rules. So that's that's the confirmation. That's confirmation that that's what they'll be doing, but we haven't got the confirmation of what those rules will be just yet. In the first phase, players will compete to maximize their placement in the players cup qualifier. So that is going to be an online event like an international challenge, which will be run over a weekend, you know, so run from Friday to a Sunday evening. You're going to have 15 battles per day and you're going to be able to try and get as high rank as possible. Normally something like 1700 is pretty safe. If you can rank up to that pretty safe and then you can stop and you can be pretty sure and known that you've qualified in your region. That may vary, of course. Don't take that as verbatim. So which will take place from Friday, April 9th through to Sunday, April 11th. The top players by rating zone after removing ineligible players will advance to be able to register for the Pokemon players cup regional qualifiers. Players must have opted into the player Pokemon terms of use and have their player ID. Players will also need to link their Nintendo account to their Pokemon Trainer Club account before the competition is eligible. So this is the biggest takeaway from this video that you will have. If you're going to listen to me about anything before entering this tournament, please let it be this one thing on this page. It's in the description. I'll link the page to go and link your accounts as well before you register for the tournament. What you need to do is make sure that your play account is linked to your Nintendo account and you can do this through this link here. It will take you to another page and it will take you step by step through how to do this and make sure because if your accounts aren't linked, then you will be ineligible player.  So please remember to do this before you register for the tournament, okay? So the first phase is obviously the qualifying stage and the qualifying players from each region. North America going to have 256 players, Europe 256, Latin America 256 and Oceana 128. So in June and July, these players will compete in a regional qualifier. So the players that qualify from this online tournament here, the top 256 from each region excluding Oceana 128 will then progress in June and July to complete in their respected regional qualifiers within their region ratings zone. For new players, CUP will use Swiss pairings for the first weekend of regional qualifiers. Now, this is the other big bit of news. Swiss rounds are being introduced to the tournament where it was just a loser's and winner's bracket. So if you lost twice, that was it. At least with Swiss, it's kind of gone along the same lines but the pairing system is a lot better. It's a better system in general. So really welcomed and I know the community on the whole is really welcoming this. So massive step forward, big props to play Pokemon for introducing this. So Swiss parents will be the first weekend of the regional qualifiers. Players will be required to register their team online before the first regional qualifier date and will need an account with both Discord and Battlefy to participate. So make sure you do get those things. Sure, that information will be reiterated if you do end up qualifying. Matches will be best of three. Excellent news because the qualifiers, unfortunately, are still going to be best of one. That online tournament to qualify is going to be best of one. Matches will be best of three, like we've just said. Specific details on rules and report times will be available closer to the date. So that information will be released closer to the time and then advancing players will be contacted by email with the next step and registration information once results are finalized. It is essential that the email address on your Pokemon Trainer Club account is accurate and up to date in order to receive this communication. It kind of goes without saying, right? But just check it. Make sure if you're competing in this, make sure that your email's up to date because if they're trying to get in contact with you about playing in the tournament and your email's wrong, obviously, you're not going to get it. You're not going to be able to compete and you're probably going to kick off on social media like many players do about not getting things right. It's your responsibility. Make sure that your information's right on the Play Pokemon page. Just make sure just check it. It's worth doing, right? If you require assistance updating your email, please reach out to customer support. So you've got help if you need it as well. But just make sure that that is up to date. Like I say, it's kind of self-explanatory, right? Pokemon Players Cup regional qualifier schedule. So it will be the 19th of June. Up to nine rounds of Swiss will be played in the region. Each region, the top 16 players in each region will then advance to the corresponding region finals, which will be held on July 3rd. Region finals will be a new seeded double elimination bracket based on previous weekend's final Swiss standings. Play occurs until four players remain in each region, which is very exciting, you know? So we're going to have that stage, the region finals, all going to be seeded double elimination bracket. And then the four top players remaining in that event will then move on to the global finals. The players handbook and email communication will provide the specific play time for each region, which will be announced closer to the date of the event, which will be closer to June and July. I'm guessing players will use the same team for both phases of regional qualifiers. So when you're locking a team for your region qualifier, potentially if you progress to the regional finals, you're not going to be able to change team until the global finals. Moving on to the global finals. So 16 players in total, four players from each region, top-performing players, all progressing to this stage of the tournament. Global finals will be a new double elimination bracket. The players will be able to submit a new team list, like we just mentioned. The global finals will be played on the 17th of July, times to be determined and sent to finalists by email. So that will be confirmed near the time. And eligibility is the final thing that we'll look at. Final players will not be eligible to participate in regional qualifiers. So it will be basically players born in these years, obviously junior and senior divisions. Just make sure you check that out. Players who reside outside countries not supported by following player Pokemon rating zones. So outside of North America, US, Canada, Europe, Latin America, Oceania will not be able to compete, which is a little bit of a shame, but like I said, it is what it is the minute. Players who have not opted into the player Pokemon terms of use, make sure you do that. Mention it earlier on the video. Just make sure you do all the steps before you sign up and before you take part in the tournament and players who are unable to abide by the BGC tournament rules, which is again, self-explanatory. No one needs me to go over that, you know, just play by the rules or you're not going to take part. So that's pretty much the bulk of the information. Now, once you've adhered to the terms and conditions, once you've linked your Nintendo account to your Trainer Club account, you're all set to kind of jump into game, okay? And then once you're in game, turn the lights on. What you want to do is come over to the versus option here on your menu screen in your copy of Pokemon Sword or Shield. Go on to the Battle Stadium and you'll be taken on to the kind of the main menu screen here and this is where you want to be going in game to register for the qualifying phases, which are going to be on the 9th of April to the 11th. So you want to come down. Online Tour competitions is the one that you want. And here it will say I've registered my card already. So participating in official competition is the one option that you need. It will say accepting entries right now. You want to click into that and then it'll take you through all the steps that you need to do to enter yourself into the qualifying stages. And you can see here I'm already entered Pokemon Players Cup 4 qualifier, which will be taking place from the 9th of April to the 12th online, but it is the 11th. You're going to get 15 games per day on the Friday, 15 on the Saturday, 15 on the Sunday. If you can't play them all on one day, they can roll into the Sunday and you can play 45 games like some mad person on the last day trying to qualify. Like I said, you don't need to complete all the games. Just get to a certain rank and where you feel safe enough to think I've qualified and then you can give up and just sit back, relax and wait for your email. So that's what you need to do in game. Hopefully all the stuff that I've kind of covered is really helpful. If you've got any questions, reach out in the comment section below. Let me know because I'm more than happy to kind of help players out getting things sorted, but I've went through each step specifically in this video to make sure that you know what to do in what order. So don't register your online game for the qualifier until you've done all the steps with your club account. Terms of use and things like that prior to doing that. Okay, so because if you do it afterwards, then there'll be complications. You're going to have to raise tickets. You might not be an eligible player even if you get the rating that you want. But very exciting. The Swiss rounds being introduced is a huge step forward. The prizing is a huge step forward. It's going to be very exciting. Obviously, it's really nice to have the continuation of players Cup 4 as well. Hopefully you found this useful. If you're taking part as well, let me know down in the comment section below. I would love to hear if you're planning on taking part in players Cup 4. Even if you're not in VG, if you're going TCG or poking, going to be very exciting whatever you do. But the fun continues with players Cup. So I hope you're all looking forward to it. Hope you found this video useful and I'm going to wrap it up there, friends. So thank you as always for tuning in. Have a great rest of your day and I'll catch you all for another episode very soon. So until then, take care and bye bye.


Hello, I've driven about nine hours north from State College into the northern part of the Adirondack Park in upstate New York. And I'm here to visit my sister, who I've just skied with out on the middle Saranac Lake. In the background you can see one of our favorite mountains, Ampersand Mountain.  But I thought that while I'm here, I would take advantage of the wintery weather that they're experiencing here that we're not having in central Pennsylvania to talk to you a little bit about climate and also about the hydrologic cycle and some of the ways in which the forests interact with the critical zone during the winter season. The difference between weather and climate is an elusive concept for some people. Now I'm going to try to describe it to you. Recall that just moments ago the sky was clear and the sun was out to the east but now we're in the middle of a nice snowfall. This is an example of the weather. Weather to me describes the physical conditions in the atmosphere and those conditions can change rapidly on timescales of hours to days from region to region and also through time. On the other hand, it describes prevailing weather trends in a region typically considered over years to decades. So while the weather is different today between the Adirondacks and central Pennsylvania both regions are characterized as having a humid temperate climate. One of the things that's unique about the Adirondacks compared to central Pennsylvania is the mountains and the topography and the elevation. So this geographic component is important to understanding climate so mountainous regions further from the coastlines typically have colder, longer winters than areas closer to the coast at lower elevations like central Pennsylvania. In mid to high latitude regions that experience a truly cold winter season critical zone processes slow down and in some cases cease to function. For example, in the frozen Adirondacks the water that in other seasons would percolate into the subsurface's groundwater and flow through the rivers and lakes of the region is temporarily stored as ice and snow at the surface until temperatures warm, thaw occurs and critical zone processes begin anew. We'll reconsider seasonality in later lessons when we discuss the hydrologic cycle and biotic functioning of the critical zone.


Namaskaram Swam. The other day you had mentioned that thought is very necessary for one to take any action. Sometimes I feel the action I've taken is based on a thought that's not mine. Is that possible for someone to plant a thought in my mind, making me think it's mine? Then, none of your thoughts are yours. None of your thoughts are really yours, please see. Thought is something that you generate from implanted information, all kinds of things hitting you. The way you think right now depends on what kind of family you were born in, what kind of parents you had, what kind of education, what kind of society, what kind of social backgrounds, religious backgrounds and all these things deciding how you think. Yes or no? For sure, isn't it? So how can you say it is your thought? All kinds of people are working. Can somebody plant a thought? Definitely. Definitely, yes. If you're talking about someone consciously wanting to plant a thought in you, is that possible? Very much possible. But you shouldn't get into this mode because every time you do something wrong, you will think, somebody planted this in my… even if you let somebody plant it in your head, it is still your doing, isn't it? Yes? You let somebody plant a thought in you, that is also your doing, isn't it? Or somebody planted a thought in my head, what can I do? People are going about this, this has become a fashion everywhere. This is an Indian thing. When Indians got very affluent many generations ago and they got naturally lazy, they came to this, God willing. Anything you ask them, they'll say, God willing. God willing, I will get up. Who knows when goddamn God is willing? If I do it, God was willing. If I don't do it, he's not willing. This is a horrible trick, but it goes on in the world. Everything that matters to them, anyway they will do. If you ask something, they'll say, God willing. Yes? Will they say, if God willing, I will have my dinner? No, they will eat. If you say, can I have dinner? They'll say, God willing. So, can we plant a thought? Definitely we can. In fact, we can plant a whole philosophy into you if you want. Why just a thought? A whole series of thought, a complex series of thought, we can plant into your head. But there are different ways of planting a thought. There are dark ways of doing it. There are straight ways of doing it. There are other ways of doing it where a thought is not planted, you are made to think in a certain way, purely for your well-being. This needs to be done. Otherwise, you will just scatter yourself all over the place and spend your life without any purpose, without getting anywhere. The dark ways of doing it involves very various dark arts through which they will plant negative thoughts in your head where you will work for your own destruction. The straight ways of doing it or the school teacher's way, they're trying to tell you, this is better, this is better, this is better, you know, constantly. Or the marketing manager's way, the coca-cola, the real thing, the real thing, the real thing, the real thing. Now you'll say the real thing. If I say the real thing, you'll say coca. Everywhere it's written, around the world, real thing. So that is just by repetition. It's straight, if you want you can reject it. With the first one, if you're vulnerable in some way, you have no choice, it will anyway enter your life. The last way of doing it will happen only if you're willing, open and receptive. Otherwise, that person who does the last way of putting thoughts into you is not even interested in doing such things. Only if you are willing, open and you want to go in a certain way but you do not have the necessary grit to hold on to something that you need to do, then a thought can be implanted in you in a different way. So if you're talking about negative thoughts being implanted into you, all you have to do is bring some simple meditation or something where your system gets organized in such a way that these things cannot affect you or you must carry something with you which will create a certain cocoon of energies around you where these things cannot affect you. There are various ways of preventing somebody else influencing your thought. So, I am also willing to plant a thought in you, more than a thought in you. I can plant an explosive in you if you want. Not a bomb, an explosive. You know, there's a difference. Bomb is purely destructive. An explosive can be used in so many ways, isn't it? If you want, I can plant an explosive. Why? Just a thought. If you simply say, boom, that goes. I can plant an explosive of ecstasy if you want. If you simply close your eyes, lots of people, if you just close their eyes, their eyeballs will go pop. Why? Just a thought. Thought is a rudimentary thing, very surface thing. We can plant energy into you in such a way that it guides your life wherever you are, whatever you may be. Technology is then thoughts.


So we've reached an important point in our discussion of what trigonometry is and how we're going to analyze Triangles and circles and talk about cyclic functions and take a look at what waves look like on a graph, right? And you know, we've done a fair bit so far and we'll do a little recap We'll do a little setup, but for anyone that wants to skip the setup and you've already been following the videos Just to let you know what we're about to do I'm gonna draw another unit circle here. Okay, and We're gonna create a table here and the table that we're going to create is What the three primary trig? Ratios are for the unit circle as we move around the unit circle Okay, and we're gonna create the table for the special right triangles and The four quadrants the nodes, right? For theta and radians, right? So we're gonna find out what the three primary trig ratios are for 030 1690 and multiples of that all the way up to 360 and the equivalent of it in radians, okay, and this table that we're going to create is Something that I tell all of my students that as far as I'm concerned every trigonometry test in the world the first question asked should be Generate this table and this isn't about Memorizing this table a few because if you're trying to memorize mathematics, you're gonna fail Mathematics is not about memorization. It's about understanding. It's about using right? You don't memorize a language. You learn how to use a language mathematics is the same thing especially when it comes to This table that we're about to generate, right? So this isn't about memorizing this table This is about learning how to generate this table and I'm gonna take, you know Fairly long time explaining how we get all the answers get all the ratios or the three primary trig ratios for the unit circle in This video and then what I'm gonna do I'm gonna produce there's two more videos coming of the same thing and one of them is gonna be a little bit longer than the other one and yet The shortest one is just basically me without giving any commentary and just generating the table and what you should do is If if you know how to generate this table, then fantastic we can continue on with What you know our discussion of trigonometry if you do not generate this table You need to take the time to learn this table and this table basically talks about You know what our ratios are for a unit circle what the three trade ratios are how we convert between radians and degrees What the value the x-coordinate and the y-coordinate are for us moving around the unit circle and these are all really sort of the basis of what we need to know before we can actually start using trigonometry, right? start looking at certain systems, okay, and I'm making these three videos basically because I want there to be a you know extended discussion of How to generate this table and then there had there needs to be a video of walking through how you can do it rapidly and One as a sort of a quick review for anyone about to writing the test of how they go about doing it, right? Because what I what I do actually tell my students is whenever they're writing trigonometry exams for grade 12 specifically higher level trig, right? When they get their tests for them just to put their name on the test, right? so if you're writing a trig exam as soon as you get the test you put your name on the test and you put that test aside and The first thing you do is you take one of the scrap pieces of paper available to you and you generate what we're about to generate Okay, because that information is going to Prevent you from making any silly mistakes during the test And it's also going to provide a lot of the answers to a lot of questions in most trigonometry tests, right? Because if you know how to generate this table, you understand the three trig ratios You understand the unit circle you understand degrees you understand radiance how to switch between the two You understand what the trig ratios mean, which are basically your x and y coordinates, right? So basically by learning how to generate this table you Understand almost everything we've talked about in the previous videos and now sort of a critical point where we can progress further, right? Because as soon as we understand this as soon as we know how to generate this there's two different avenues We can go and trigonometry one of them is sort of We did a little teaser. Well a long teaser when we graph the trig Functions right when we graph the sine cosine and tangent functions So one thing we're going to do when we finish, you know Learning how to generate this table is go down the avenue of taking a look at trig functions And how they you know how they model certain systems and start graphing certain system, right? The other branch you can go down and trigonometry is taking a look at trig identities And we will do that as well, right? So as soon as you learn this How to generate this table there's two two different avenues you can go in your study of trigonometry And it's up to you which direction you want to go For me, I'm going to take a look at the functions first and then we're going to look at the trig identities because Trig identities is more playing with the language and the relationship between the different ratios in the unit circle The trick functions take looking at the trick functions and how to graph them and what they represent is more taking trigonometry Applying it in the real world and taking a look at certain systems that want to analyze, okay? So that's what we're going to do for anyone that wants to skip the setup for now What we're going to do is I'm going to create another unit circle here I'm going to set up my table here and there's going to be you know a little reminder here that At the information we're going to present here in shorthand and short form for us to generate this table And what we're going to put on this page is what you need to be able to generate Before you write any major trigonometry test, okay? So first thing we're going to do is Create another circle, right?  We got the loop here. I think the loop is getting pretty tight there And I'm going to throw this guy on here and then we're going to go around, right? So let's go down again. I think this was 24 done enough. I should know what it is, right? So 1 2 3 4 5 6 7 8 9 10 11. So here's 12 and then we're going to go 1 2 3 4 5 6 7 So what we're doing now is a little bit better This other pen, so an off-circle a little bit, but that's okay Can't make it all perfect, right? So Now that we've got the circle set up, let's go Set up our grid. Yeah Because that's what we want And we're going to set that up Using our little lever again, right? Green axis here X axis here So what we're going to do we're going to talk about theta and degrees radians sine cos and tan and these are going to be our rows, right? And what we're going to do I'm going to create the table, so I'm going to leave a little space So let's do this We got this, we got so what I've done so far is Generate it our unit circle, the circle put it on a Cartesian coordinate system, right? And what I've done is created a table and usually This table I generate, you know, it's one long table, right for going from zero degrees all the way to 360 degrees But because we're limited on the space that we have here I've broken this down into two segments, right? And what we're going to do we've broken this thing down into the rows being radians degrees sine cos and tangent, right? our three primary trig ratios angle and degrees and angle and radians and What we're going to do we're going to walk around The unit circle so we're going to start off here, right? As we have in the past videos, right? And we're gonna move around The circle, right? And we're going to look at what happens to our three primary trig ratios As we move around the circle, right? We're going to look at the ratios and the ratios as we've talked about before as we move around this, right? If this is one two three four five six seven eight nine As we move around let's say we go here Right we end up here The three the two primary trig ratios anyway the sine and cosine are just basically our y and x-axis, right? Our x-axis being cos theta our y-axis being sine theta, right? As we've talked about before So what we're going to do we're going to take a look at our coordinates, right? As we move around the circle, which basically means we're going to take a look at what our y-value is and and what our x-values are going to be, right? At each of the stops for the special right triangles and the nodes, right? And it's gonna be you know, we're gonna record it all figure it out Throw it on here, right? And what we're going to need to do is know how to generate this before we continue on in studying trigonometry, right? Because once you know how to generate this it means you understand everything else we've talked about previously and that's the key, right? We just built the foundation of trigonometry, right? And what we're doing right now is Saying that we know how to you know what it's all about What the what the trigonometry what trigonometry the system is, right? We're we're stating that we understand how triangles are related to circles We're stating that we understand what it means to move around the circle, right? How our coordinate changes We by generating this we state that We understand what a cyclic function is and how wave graphs, right? And we're going to do it again for radians because we've already sort of jumped the gun and graph sine cosine and tangent for theta and degrees where we're going to do the same thing again after we generate this table For radians, right because we're going to mainly work with radians So I can't emphasize this enough For us to progress in studying trigonometry either going down The the path where we're going to look at functions graph functions and take a look at how cyclic functions You know, we can manipulate cyclic functions or how cyclic functions Are related to you know the unit circle trigonometry, right? or if we're going to go down the road of Trig identities, right? We're messing around with the system and seeing how things are related, right? No matter which branch you're going to go off You need to be able to generate this table Okay, and as I stated before as far as I'm concerned the first question on every trigonometry test should be Generate this table not memorize but generate because if you're memorizing this it doesn't mean it means nothing really. It's You're not saying that you understand the system You're just saying that you know how to memorize something now the question is do you know how to use this, right? And the reason the first question in every trig test should be generate this table is because We're going to use this table for almost everything we do from now on Right, so instead of trying to always do single calculations Right figure out what a certain ratio is what we're going to do is we're going to have this table as a reference, right? So when given a certain the radian we can find out what it is in degrees We can find out what the trig ratios are right when given a certain trig ratio We can go up and find out how that stuff is related to the other trig ratios as well as the angle and Degrees and radians right so it's going to be really handy and most trig tests that you end up writing a Lot of well many of the questions Are just basically this table parts of this table be an answer from this table, right? Then this is basically for our special triangles as the nose So what we're going to do is we're going to Lay down the degrees first because that's the one we're really familiar with right and As we talked about the first degree. We're going to look at is Zero and then we're going to go to 30 degrees 45 degrees 60 degrees and 90 degrees, right? And that's the first quadrant Right, so we're going to go with theta in degrees is going to be 030 45 60 and 90 right and One of the most beautiful things about trigonometry is not that well for sure that it it's Circles it represents the ideal cyclic function that once we start here We go all the way around We do it again, right? So as long as we understand one rotation we understand every other rotation, right? So Circles unit circle is a cyclic function it repeats. So there's huge symmetry within this, right? one of the other beautiful aspects of a circle is is if we understand what's going on in this quadrant then we understand what's going on in The other three quadrants with slight modifications, right? Because this thing This quadrant here we can just mirror it here and then flip it down and then flip it down And that's what's gonna happen for this table all we really need to learn is what happens in the first first quadrant because everything else is Sort of copied from this is generated from this With it either being positive or negative right or changing the sign being negative because all of the stuff in this quadrant is positive, right? so What we're going to do is Learn what's gonna happen in the first quadrant and then take a look at what happens in the second third and fourth And you'll see the beauty of it how symmetrical it is, right? So the first angles we had we had zero degrees 30 degrees 45 16 90 The next special angle that we have on our unit circle is we're gonna go 90 and we're gonna add 30 Right, and then we're gonna add 45 and then we're gonna add 60 and then we're gonna add another. 90 right? And then we'll get to 180 we're gonna add 30 we're gonna add 45 We're gonna ask 60 and I'm gonna have 90 when we get to 270 we're gonna add 30 We're gonna at 45 we're gonna ask 60 and we're gonna 90 or back here, right? So that's how we're going to generate the rest of the angles in degrees, and they're just basically multiples of the first quadrant, right? So from 90 degrees, right, from here, we're going to go 30. So 90, we're going to add 30 degrees. So that's 120 degrees, right? And whenever I'm generating this table, whenever you generate this table, you're going to need both hands, okay? Or you're going to have to be able to, you know, have a good track with your eye, because all that's going to happen is we're going 90 plus 30 is the next special angle. And then 90 plus 45 is 135, right? And then 90 plus 60 is 150, and then 90 plus 90 is 180 degrees, right? That's how we generate the rest of the angles and degrees, okay? And we're going to do the same thing in these quadrants, right? Because we're 180 degrees, and then we're going to add 30, which is 210, right? Now, again, I usually generate this table when I'm working with it on one piece of paper from, you know, zero degrees to 360 or zero degrees to 360 degrees, all in one shot, right? That way I can scan it and go down the table and pick things off, right? Because we're limited on space, we're going to have to have, you know, break it up into two pieces. And by doing that, what I have to do is make this column the 180 column as well, okay? So keep this in mind. This guy, when you're generating in one sheet, and we will do it in one column or one table, this guy is just an overlap of here, okay? So this guy is going to be 180 degrees, right? And then we're going to add 30. So 180 plus 30 is 210. 180 plus 45 is going to be 225. 180 plus 60 is 240 degrees. 180 plus 90 is 270 degrees, right? And then again, we're going to add 30, 45, 60. So 270 plus 30 is 300. 270 plus 45 is 315. 270 plus 60 is 330. 270 plus 90 is 360. And that's how you generate the degrees column as we move around this thing, right? And if we're going to, you know, I'm not going to put on the lines here because it's going to get really busy, right? But what we're going to do, we're going to put the ticks for the x's and y's, right? So basically what we've done right now is let's just draw the little dots of where we are, right? So this one is going to be 30 degrees if we do one triangle here. And then we've got 45 here. And then 60 is going to be about the same distance here. So let's do here, here. Yeah, so it should be one, two, three, four, a bit, right here, okay? And let's generate the trig ratios for these guys. And then we'll continue the dots around and you'll see how that stuff lines up for the x's and y's, right? So what we've got right now is we need to figure out what our trig ratios are for these guys, right? Now one thing we're going to have to do to give us a reminder because I don't like memorizing, go into memory every time and picking out what the special triangles are, what the ratios of the special triangles are, what their sides are, what the unit circle is because I'm not going to draw a unit circle like this exactly every time I'm going to work with the trigonometry, right? Whenever I'm going to generate this table, I'm just going to make it shorthand, right? Really fast. So what we're going to do up top here is we're going to throw just a circle here, very simple. But it's going to remind us of what we're really working with, right? It's a good trigger for your memory to kick you into trigonometry mode, okay? So what we're going to do, we're going to draw a unit circle here. One, two, three, four, five, center. And I'm going to do this. I'm going to try to generate this as clean as possible. So let's go here, here. So let's throw a unit circle on here. Let's see. Yes, use this guy. It's hard to do. I tried it once before doing it with the floss, with doing a little circle. Very difficult, very difficult, right? So I'm just going to do this. Hopefully this comes out cleaner, right? So we have a unit circle here, okay? And this point here is going to be one and zero, right? This point here is going to be zero and one. This point here is going to be negative one and zero. This point here is going to be zero and negative one, right? As we've talked about before, if this is a unit circle, the radius is one. And those are the coordinates for your x and your y-axis.  And your y-axis happens to be sine theta, right? And if you need a reminder, you can put that down. You can say this is cos theta and that's sine theta, right? The other thing we need, we need our two special triangles that cover 30s, 45s, and 60 degrees, right? So I'm going to plop this down here as well. Let's do... So these are our two special triangles. And, you know, for lack of a better word, this is something you're going to have to memorize. But it should be something that you've used a lot. So it should be, you know, more instinct of generating this than anything, right? So the special triangles should be 30, 60, and 90 degrees, right? And across from the smallest angle, we put one. Across from 60 is going to be square root of three and across from 90 is going to be two, right? And 45, 45, 90 degrees. 45, 45, 90 degrees is going to be one, one square root of two, okay? And we talked about how you can generate these things, right? So it's not really that you're memorizing it, it's that you understand that you've worked with it enough that you know it. So what we're going to do now is take a look at what sine of zero degrees is, 35, 45, 60 degrees and 90 degrees is. And then we're going to generate the radius for this and the other two trig ratios cos and tan for this, right? So let's do sine theta first, okay? Sine of an angle is opposite over hypotenuse, right? So let's just draw one triangle here. So every time we refer to it, hopefully you're familiar, you're comfortable with it. And we've got something that we can point to, right? So we're going to take a look at sine theta first. And this is our angle here, right? And standard position, right? All the terminology we've learned. So sine of zero degrees, sine is our Y, right? So if we're at zero degrees, this guy is flat, right? The terminal arm is right there. So sine of this is what the Y value is when you're standing here. And when you're standing here, your Y value is zero, right? Sine of zero degrees happens to be zero, right? Sine of 30 degrees, right? What we're going to do, we're going to look at our special triangle, right? So for the nodes, for zero degrees, 90 degrees, 180 degrees, 270 degrees, and 360, we're going to look at the unit circle, right? For the other angles and multiples of them, 30, 45, 60, we're going to look at the special triangles. So sine of zero degrees, we're here. The Y for this at this position is zero, right? So sine of zero is zero. Sine of 30 degrees is opposite over hypotenuse, right? Y over R, right? So it's one over two, so it's a half. So sine of 30 degrees is one over two. Sine of 45 degrees is one over root two. And if you want to rationalize the denominator that we've talked about, it's root two over two. So I'm going to write down one over root two because I'm comfortable with working it that way. When we maybe we'll switch it up per 45, right? So this is going to be one over root two. Sine of 60 degrees is root three over two. And sine of 90 degrees, we're not using the special triangles anymore. We're going to use a unit circle. So we're up here, right? So 90 degrees, we're up here. And our Y value for that for a unit circle is one, right? So sine of 90 degrees is one. As for what these numbers mean, a lot of people I found they have a, it's sort of difficult at first trying to appreciate what these values mean. But if we're talking a unit circle, right? We're talking a unit circle, our radius happens to be one, right? So this point here is one and zero, right, as we laid out here. And as we're moving up, our Y value is increasing, right? Maximum point we can go to is one, right? So this is zero and one, right? We're standing. So what the trig ratios are is where we are on the Y axis. So when we're at 30 degrees, the Y coordinate is one over two. So here is a half, right? That means this point here is a half. So let's take a look at what our cost value is, right? How far along we are on the X axis, right? Costs of zero, we're here, right? We're here. Our X value is one, right? Our X is one, so cost of zero is one. Costs of 30 degrees, we have the special triangles, adjacent over hypotenuse, root three over two. Costs of 45 degrees is adjacent over hypotenuse, one over root two. Oh, sorry, yeah, one over root two. Costs of 60 degrees is one over two. And cost of 90 degrees, 90 degrees we're up here. Our X value has gone down to zero, right? And then we're going to go into the negative part, but we've gone to zero. Our X value is zero. That means cost of 90 degrees is zero. Now, one of the first symmetries you should be noticing right now is that costs and sign are mirrors of each other, right? Because if you take a unit circle, if you take a circle, really, and this is our Y axis as our X axis, if you rotate this 90 degrees, the X axis becomes the Y axis and the Y axis becomes the X axis. So it's sort of a mirror of each other, or a rotation, right? So one symmetry that we have when we're generating this table is when you generate the sign values, all you have to remember is the cost mirrors the sign. With the center point being the axis of symmetry, really, the mirror, not the axis of symmetry, but the mirror point, well, axis of symmetry as well, but the mirror point being 45. So when sign is one here, cost is one here, root three over two, root three over two, one over root two, one over root two, because that's our mirror point, one over two, one over two is zero, zero. So they're sort of, you know, mirror of each other, so as long as you can generate sign, you can generate cost, if you don't want to look at these guys, right? Now, 10 is sign divided by cost, and it also happens to be opposite over adjacent, right? So we can generate the 10 ratios from either taking sign and dividing it by cost, right? Or looking at the special right triangles. I use both for this, because for the nodes, for 0, 90, 180, and 270, I use the division, sign divided by cost. For the other angles, 30, 45, and 60, I use the special right triangles. I use these two guys. So 10 of zero degrees is sign divided by cost when we're here, zero divided by one is zero. 10 of 30 degrees is, I go to the 30 degree special right triangle. 10 is one over root three. 10 of 45 degrees is one over one, opposite over adjacent, right? So it's one, one divided by one is one, right? 10 of 60 degrees is root three over one. So it's root three. 10 of 90 degrees, I'm gonna note, I'm at the top of the quadrant here. So I'm gonna use sign divided by cost and one divided by zero is undefined. We can't divide by zero, right? One of the limitations we have in mathematics, right? So one divided by zero is undefined. So we just figured out what our three trig ratios are. As far as what the cost numbers mean, well, they're the same as the sign values, right? Oh, we forgot to put these sticks in, right? So we'll do this right now. So for the 30 degrees, so for the 30 degree angle, when we're at 30 degrees, our Y value is one over two, right? Sine theta is one over two. Cost theta is root three over two. And that's just the number, right? That's the square root of three over two, right? So if we grab a calculator, what does that mean? Square root of three over two. Let's bring out the trusty solar calculator. This thing keeps on ticking. So three square roots, where's my square root? Square root of three divided by, so square root of three is 1.73, right? 1.73. So that's what the square root of three is. Divide that by two, divide that by two, is 0.8660 dot, dot, dot repeating, right? So that's just that number is a coordinate system, right? So when I write down our coordinate here is square root of three over two and one over two, right? All I'm saying is on a Cartesian coordinate system, when you're moving around a unit circle, a circle with radius one, if you're 30 degrees up, right?  That's all it means, okay? And for the 45 degrees when you're standing here, and this is our 60 degrees, when you're standing at 45 degrees, sine of 45 is one over root two, right? So your, this value here is one over square root of two and the cos of 45 is one over square root of two, right? So cos is one over square root of two, one over square root of two and that's, I think it's 707, let's do this. So one divided by two sine of function square root is 7.071 dot, dot, dot. So your coordinate here is your x and y are, your x is one over root two and your y is one over square root of two, right? When you're at 60 degrees, right? Your y value is your sine theta square root of three over two and your cos is one over two, right? It's the flip of 30 degrees, right? So this coordinate is one over, oops, one over two and your y is square root of three over two. So here we're at square root of three over two and here we're at, so now that we did the three trig ratios we found out what our coordinate system is in the first quadrant as we move along these angles. Let's take a look at what these angles are in radians and we've talked about this converting between degrees and radians and I showed you the long way to do it with the ratios especially you need to use that if you don't have special angles. The other way I showed you was multiples of pi, right? So that's what we're going to do to generate all the radians for all of these degrees. So what we're gonna do right now is generate the radian column since we're on it, okay? So zero degrees in radians is zero. You're at zero radians. We know that already, right? 360 degrees is two pi, we know that already. 180 degrees is pi radians, right? Half of 360 if you go full rotation. 360 degrees means two pi radians and we talked a lot about this already. That means 180 degrees is pi, right? So 180 degrees is pi. Now, in the first quadrants we can get to all of these angles 10 degrees from 180, right? So to find out what 30 degrees is in radians we look at 180 degrees, right? So we ask ourselves, what do we do to 180 degrees to get to 30 degrees? What do we do to 18 to get three? We divide 180 degrees by six, right? 180 degrees divided by six is 30 degrees. Well, the beauty of mathematics is very symmetrical, right? So you're gonna divide 180 degrees by six to get to where you wanna be, which is 30 degrees right now. Then we're gonna do the same thing to radians. So pi over six is 30 degrees. 45 degrees, what do we do to 180 degrees to get to 45 degrees? We divide it by four. There's four 45s and 180, right? You go one, two, three, four 45s, right? Well, if we're gonna do it to 180, we're gonna do it to pi. So 45 degrees is pi over four. What do we do to 60 degrees? What do we do to 180 degrees to get to 60 degrees? We divide 180 by three. We do the same thing to pi. So pi divided by three is 60, right? Pi over three. 90 degrees, we divide 180 by two, right? So we're gonna divide pi by two. So 90 degrees is pi over two. Now, all the other angles, 120 all the way to 330 are multiples of 30, 45, 60, right? Because that's what they are. We're moving around with the same displacement and the angles anyway, same angle changes, right? So that's exactly what we're going to do. So what we're going to do to find out what these angles are in radians, we're gonna look at the first quadrant and we're gonna multiply the angles in the first quadrant by something, right? So we ask ourselves 120 degrees. We can't get to 120 degrees directly from 180, right? Well, we can but it's a fraction. We wanna make the calculations easy, right? So we go to 120 degrees and we ask ourselves, what do we do? How do we get to 120 degrees from one of these angles, 30, 45 and 60? Well, we could multiply 30 by 40, 30 by four, that gives us 120, right? So that means in radians, we do the same thing. This would be four pi over six, but then we have to reduce the fraction. So what we do, we go to the biggest number that we have to get to 120 degrees. So 60 times two gives you 120. So we're gonna do the same thing to pi over three. So pi over three times two is the same thing as 120 degrees, right? So 120 degrees in radians is gonna be two pi over three. Now to get to 135 degrees, 135 is multiples of 45, right? And we multiply 45 by one, two, three, right? Just 345 is 135. So I'm gonna multiply pi over four by three. So 135 degrees is three pi over four, okay? 150 degrees, the only number I can use from the 30, 45 to 60 to get to 150 directly with one multiplication, one integer, right? It's 30 degrees, so 30 times five gives me 150. So I'm gonna multiply pi over six by five, which is five pi over six, right? Now 180, we already know what it is in radians, right? So that's just pi. So this column is just gonna be everything the same as this column. 210 degrees, I'm gonna multiply 30 by seven, right? Three times seven gives me 21. So 30 times seven gives me, so it's gonna be seven pi over six. 225 degrees is multiples of 45, and I always do this for 45. I never can do it by memorization. So 45 times one, two, three, four, five. 45 times five gives me 225. So five times five pi over four. So five pi over four is 125 degrees. 240 degrees, I get there from 60, okay? So six times four gives me 24, right? 60 times four gives me 240. So I'm gonna multiply pi over three by four. So 240 degrees is gonna be four pi over three. 270 degrees is 90 times three. So it's gonna be three pi over two. 300 degrees, I can get there with 30 and with 60. I'm gonna go there with 60 because that way I don't have to reduce my fraction, right? So 60 times five gives me 300 degrees. So 300 degrees is gonna be five pi over three. 315 degrees is multiples of 45, right? So I was at 545s when I was at 225. Five, six, seven, right? One, two, three, four, five, six, seven, 45s. So it's gonna be seven pi over four. And 330 degrees, I'm gonna get there using 30 degrees. 30 times 11 is 330. So 11 times pi over six, so 11 pi. And then we have 360 degrees, which is two pi. And one thing you should have noticed here as well is the symmetry within this, right? Because all we're doing is sort of doing a rotation like this. We're going to 90 and then we're coming back. So what's going on here is, so what's going on here is we're going to 90 degrees, right? And then we're going boom, boom, and then 180, okay? And then if we're here, if this was one column, we're 180 and then 270, sorry, 210 and 150 are multiples of pi over six. 135 and 225 are multiples of pi over four. 240 and 120 are multiples of pi over three. And then we're at 270, right? 270 on either side, we're multiples of pi over three, multiples of pi over four, multiples of pi over six, okay? There's a lot of symmetry within this table. That's why it's really easy to generate. And it's not really about memorization, it's about appreciation, right? It's about generating it. And the reason this symmetry exists is because let's do 90 degrees here. If we're at 90 degrees, 60 degrees and 120 degrees are going to have the same magnitude up on the x-axis and the same magnitude along, sorry, same magnitude up on the y-axis and the same magnitude along the x-axis, right? So if we're sitting here, if we're sitting here and this is 120 degrees, right? Our x-value, our y-value is again, three over two, right? That's our horizontal, we're right there. Our x-value, if you come down, that's going to be the same distance along as it was in the positive direction, right? So our x-value here becomes one, two, three, four and a half. Our x-value here becomes one over two, it just happens to be negative, right? Because we're in the negative x quadrant, right? So our coordinate system here is, our x is negative one over two and our y-value is root three over two, okay? My red pen is dying. Let's see if we've got a better red pen. When we're at 45 degrees, we're here, our y-value is going to be the same, right? If we're standing here and our x-value is going to be the same distance along on the positive x-axis as it was in the negative x-axis, right? So if our x-value here is going to be one over root two, but negative, so our x-value is negative one over root two and our y-value is one over root two, right? That's the symmetry that we see. When we're standing here, when we're going across, we just went 30 degrees on either side of the 90-degree angle. So our y-value better be the same and our x-value is the same, right? The next one is 45. We've gone 45 on either side and then we're here. Our y-value is the same and our x-value is the same. Next one is 60 degrees on either side of the 90-degree angle, right? Well, 60 degrees is going to bring us back to 30 and it's going to bring us to 150 degrees, right? If you see it here, you're at 150 degrees, okay? Oh, sorry, right here. We're at 150 degrees, right? Right here. And that's the beauty of the symmetry, right? And our x-value is going to be negative square root of three over two. I'm just reading it off here. I'm just making it negative, right? And our y-value is going to be one over two. So this is negative square root of three over two and that's one over two. And that's what we're going to do right now is generate these guys, right?  So sine of 120 degrees is root three over two. Sine of 135 is the same as sine of 45, right? Sine of 135 degrees, you're here. Well, that's going to be the same value as sine of 45 degrees, right? Same y-value. One over root two, she's lose. One over square root of two, right? Sine of 150 degrees is going to be the same as sine of 30 degrees, so one over two. And then when you're at 180 degrees, that's zero. So when you're 180 degrees, your y-coordinate is zero and your x-coordinate is going to be negative one, which we're going to take a look at, right? So right here, we're at negative one and zero, okay? Let's do cos, well, cos does the same thing. The symmetry exists from each quadrant to the next, both, well, for sine, cos and tan, right? So as soon as we generate the sine, we can generate the cos for the first quadrant and we can generate the tan. And then once we got the first quadrant here for the three trig ratios, we have the rest because it's just mirror of each other. So as soon as you hit zero, so you're coming along, you go, right? 30, 45, 60, 90, and then you go back again. So the mirror point on this is going to be a half, one over two, and three over two, right? And one, the only catch is that you have to remember is when you're in the second quadrant, your x-values are negative. That's why these guys are negative, right?  So all you do now is make this negative, negative, negative, negative, okay? The tan, same thing, same symmetry. You're at 90 degrees, on either side is gonna be square root of three, one, one over square root of three, and zero, right? And since tan is sine divided by cos, right? Then positive over negative is negative. So the tan values here are also negative. Negative, negative, negative, okay? As for the remaining stuff here, well, let's draw our circles, put our little dots. One, two, three, four. I'm just gonna line it up with this. When we're here, we're gonna be here, and we're gonna be here, right? I'm just lining them up, right?  So if I come over, one, two, three, four, a bit, oops, let's get you around here. Negative, a half, negative, one over square root of two. Negative, negative, root three, over two. Two. So it repeats again. It does a rotation, right? So all I do with this is, when I'm doing the signs, when I come to one, I go boink, boink, boink, boink. So I'm at zero. I'm just gonna copy this column down here. Zero, negative one, and zero, okay? So when I'm here, again, this guy repeats. So it's just gonna be boink, boink, boink, right? A half, right? It's just gonna be these guys, so one over two, one over square root of two, root three over two, and one, right? But this is in the third quadrant, and we're talking about signs. Sign happens to be y, so we're in the third quadrant. We moved along here, now we're down here. Sign is negative here, so all of these numbers are mirrored, but they're negatives, right? Because sign is negative. And then when I get here, I do the same thing, I go back again, right? Because what I'm doing, I'm standing here, and then I'm coming back up again, right? So I'm the same distance away as this guy, right? There's the same distance here, okay? So this guy is gonna mirror again. So 300 degrees is gonna be same as 240 degrees for the y value, right? 240 degrees, I'm here, my y value is this, 300 degrees, I'm here, my y value is this, right? So again, it mirrors. So negative square root of three over two, negative one over root two, negative one over two, and zero, right? And again, it's negative because sign is negative in this quadrant, right? As for cos, well, that was a negative one, and I go back again, right? Which is basically the same as this. So it's gonna be root three over two, one over root two, one over two, zero, right? When I get to zero, I'm just gonna mirror it again. One over two, one over square root of two, root three over two, and oops, one, and one. Now, cos, this is in the second quadrant, right? Oh, sorry, third quadrant, right? Cos is still negative, so my x is negative, so my cos is gonna be negative. This is in the fourth quadrant, I'm over here now, and my x-axis is positive, so my cos is positive. 10, same deal, I'm just gonna write these down.  One over root three, one root three, undefined, and then mirror again, root three, one, one over root three, and zero, right? Now, all I have to do is make sure it's positive, you know, figure out which one's positive, which one's negative. 10 is sine divided by cos. If sine is negative, cos is negative, then they're negative. Over here, sine is negative, cos is positive, so 10 is negative, okay? And the values here would have been, if we're drawing this, might as well put our little guy here, right? So we're here, we're here, I guess, yeah? And we're here, right? And these guys line up with these, right? And that's us moving around the unit circle, right? Generating table, and figuring out what our coordinates are, our x and y's are, where sine and cosine are as we move around the circle, right? Now, I guess I should put those things there, but my red pen is dying off, so I'll leave those guys empty, okay? And this is something that we have to learn, we have to know how to generate. And if you're writing a test for me, if I was giving you a test, the first question on my trigonometry test would be generate this table. And what you would have to do is you would draw this, the unit circle, you would draw that, and you would draw that. This is the only thing you need to be able to generate this. Because from this, you get your degrees, you get your sine, and once you have your sine, you can get your cos, because that's the mirror along 45, or you can just read it off, the special right triangles and your unit circle, right? You can get your tan, and we get our radians from the pi, from the ratios, right? And just a little note, if you wanna remember this, or understand it, anything that you see that has pi over six is a multiple of 30 degrees, right? Anything you see that has pi over four is a multiple of 45 degrees. Anything you see that has pi over three is a multiple of 60 degrees, and anything you see that has pi over two is a multiple of 90 degrees, right? So if we come over here, and we see pi over four, then pi over four is a multiple of 45 degrees. So seven pi over four means seven times 45. And what we're going to do in the next video is do one generate this table with commentary, but go through it much faster, right? I'm not gonna explain all this stuff. I'm gonna assume we know what these numbers mean now, right? So you basically what your coordinate system as you move around the circle, right? And then the second part of it, or in the next video, is going to be us doing it, generating a table without any commentary, as if you would on a test, right? Because as soon as you get your test, you're gonna write down your name, put that test aside, grab a scrap piece of paper, and generate this table, hopefully it'll take you less than two minutes to generate this whole thing, and you'll have that table beside you to answer a lot of questions during the test, right? It's gonna provide you answers for a lot of it, right? Because for example, let's assume a question would ask you, find theta in radians for when sine theta is equal to negative one over two. So all you have to do now is go to your sine theta, go across, find negative one over two. Oh, we got one negative one over two and another negative one over two. So the angle and degrees of sine theta for negative one over two is either seven pi over six or 11 pi over six, right? Easy peasy. It's one of the first types of questions you get on a test, right? Or they could ask you, give the three trig ratios for, I don't know, five pi over four. So you would come down here and go, oh, sine of five pi over four is negative one over two, negative one over two for cos and one for tan, right? They can ask you to convert 150 degrees to radians. And all you would do is come up here and go 150 degrees is five pi over six, right? We end up using this a lot, okay? In the next video, we're gonna generate this and then after that, there's two different pathways we're gonna go down. One of them is graphing trig functions, using radians mainly because we've graphed them in one of the first videos we did just as a teaser, just to see what these graphs looks like. The other path we're gonna go is taking a look at identities and seeing how identities come into play and how we can manipulate the relationship between these ratios and what we know of right angle triangles and circles and come up with exact values for other things other than just these angles, right? Other angles, right? And the way you should think about this is this basically is us creating a whole universe, right? Creating a system that explains many other systems within our reality, within our everyday lives, right? As for why this is important because cyclic functions are dominant within our experience of life, right? Within a lot of systems that we function under as well as how we perceive life, right? How we perceive reality, right? And what we're going to do is manipulate the basic cyclic function that we have which is the unit circle, the simplest wave we can think of and we're gonna see what other types of waves, what other types of systems we can take a look at. I'll see you guys in the next video. Bye for now.


Hello everybody, I'm Evo Rabbit, we're here on a set of Corsa taking a look at the new HGK car pack with the HGK F22 and the new Supra. So make sure you guys follow me on all social media which are found in the description box below. Let's get to it. So first impressions of the overall look of this F22 Eurofighter. It looks amazing with the carbon Kevlar. Definitely a very awesome looking car, can't wait to actually rip this thing. We do, it does have, you know, a V8 under the hood, so something I'm very familiar with. And like I said, the texturing and everything in this car, the interior looks totally amazing. So let's go full send. So I do not have a sequential setup, so we do kind of have to just and go back in the center, which is not very uh, what you would say the proper way to do it. But I do not have a sequential setup because I do have the Moza shifter hooked in. It's full, so loud. We are on the base tune, so we're going to go full send here, see what we can do. Probably a fourth gear course. Second gear start though. Kind of just laid out full throttle there. First impressions on that first run, that was actually a halfway decent run, if I do say so myself. So we are going to take a look at the replay. Now, like I said, it's kind of weird that I'm using it in the Moza as a sequential in a sense, but it doesn't spring back to center, so we can't just grab it. I kind of have to like pull it back into the center place, which isn't bad if you're used to it. And the first time I'm trying it this way and it seems to be working. So we'll get another run here in the Eurofighter. Harder of initiation there. I think we may have got a little bit shallow there. Let's fill that whole zone. It's kind of clutched in there. The overall not too bad of two runs. Let's go take a look at those replays and see actually where we were at. The car does look incredibly beautiful. Initiated about the two. Second hash. Just tipping our toe in that and just tipping in there too, in there. Did kind of get all the way out there. The later part of the course was actually quite nice. I do like how this car is driving and how it feels. It's definitely a very solid car and I love that's the way to Eurofighter. So the second run, I think we're a little bit better. So let's take a look at this run. Much harder to flick. That was, that was all right. We were much deeper in that zone. Kind of missed that zone. We got all the way in that zone and all the way up in the wall on that. So for the first two runs of this car, very thoroughly impressed with it and I actually like how this car is running. So let's go back. Let's go here. Let's F5 take a look at this car a little bit more in depth from the outside. I do like the gold body, goldish brown, carbon Kevlar, the clear Eurofighter wing. Got some, the radiator fans back there all working. This model is incredibly cool. Definitely love the big chunky Nitto tires that, you know, don't look like they've been used at all. And overall just thoroughly impressed with how this thing looks. Looks super cool. So we're going to switch up to the E90 or we're going to switch up to the Supra and see if we can't tackle a 2J. So the next car in the pack is of course the A90 Supra, the GR Supra, with the HTK body kit and everything on it. This car looks very, very nice. Now I do think I see a little bit of see-through in some of the inside of the modeling and stuff like that, but definitely a very solid looking car not running on Nittos. One's running on Valeno tires, Valenos. So we're going to go full set in this and see if this car has a sequential as well. We're going to make sure we adjust our brake power down and then our brake bias at 80. Okay. Turbo cars are definitely one thing I'm not super familiar with. Staying in boost as you can see trying to even don't have a car so loud. So we're going to see how this goes. I'm not sure what gear we're going to have to be in or anything like that. So full set. Really shallow. Yep. That was definitely a very shallow run. So we're going to go that run. I think it's going to be a fifth gear on this track. I don't think we need to use clutch when we're shifting. So that's a good thing. Second gear start. Maybe fifth gear is not the right gear. Nope. So this car is a lot harder to drive personally for me than the Eurofighter was. Like I said staying in boost and stuff like that is a different style of driving that I've haven't done much in a competition aspect. Unless my car has been B8s and just power on command. So we're going to stall off the line. Yep. Definitely a car takes a much, much more finesse to drive than I feel that Eurofighter. Well, the F 22 Eurofighter. This is a car that I don't think I can actually get handle on. Like I said, I'm used to V8s power on command and being able to just a lot of left foot braking. That's why all my competition cars have been V8s. So let's see if we can get this in this run. Not the line I wanted to take. High strung out 2Js are not my cup of tea. When it comes to driving, we can give it one more attempt because I don't know what boost level we're at. We'll give it one more final go. We'll take a look at the replay of it. Inside of this car looks incredible. I don't think we're at full boost. It's not going to handle this car. So we'll take a look at one of the replays. But yeah, I can't get a handle on this Eurofighter, the A90 version in this HKK pack. So definitely not my style of competition driving with the turbo lag and everything like that. It's definitely a very finesse car that I'm not too comfortable with. So I think that's good to do here for this look at this HKK car pack. Let me know what you guys think about it down in the comment section down below if you guys are using it. I think I need to learn how to drive a highly boosted car as more because I love my V8s and I love power on command. So make sure you guys find me on social media and also on the description box below. As always, I thank you guys for coming back and watching. I'm EvilRabbit. I'll see you guys on the track.


Hey guys I mean everybody it's Sunday, July 25th just before lunch. It's 11 17 a.m We are out trying to get some steps in before it gets obnoxiously hot again today 3075 so yeah, it's already 75 degrees. We interrupted a squirrel fight just now I did happen to catch one picture of one of the squirrels. I'll put it here Although I have said it before I'll say it again.  So I Think I'm too noisy Anyway, we're just taking a breather because we want to get steps in but we don't want to have to take a second shower One week at home. So we're trying not to get too sweaty We should have done this before we took showers We didn't plan it very well Anyway We're gonna go get more steps in and I'll be happy Monday morning sort of it's not morning Turn the vlog camera on today It's 107 p.m. Monday, July 26th and see things are dinging I've got the vlog edited and save rendered and it's loading right now to YouTube and as soon as that done I will write today's post for the art groups and schedule out the post for the rest of the week I am listening to some YouTube While that is going on. I also reorganized my daily. What's become sort of my daily sketchbook It's not art practice, you know this one I switched out bags Just to make things a little easier for me because I seem to mostly be doing this on the sofa and Or I kind of want to at some point take it out with me And I think this blue bag opens flatter and it might work a little better for me Using my supplies I want to bring so I Hold on to get the tripod out so I can be hands-free All right, so this is I love bags. Y'all know this should know this I've said it on camera before that little other flowered zippered pencil case while I don't use it all the time I don't want to get rid of it. I do love it and I do occasionally use it Message for my daughter, so I'll get back to her in a second anyway So I have lots of different cases around one of the things I like about the flowered case is the elastic band on the back because I can Attach the bag to the journal So I took this one which I already have and this is from Amazon somewhere if I can figure out the link I'll link it below. I sewed a band to the back of it. It has a pocket back here that you can put It was already open that you can put You know ticket stubs or little bits of paper in and then it opens And we'll open out flat and it has plenty of room for my pen my watercolor palette my Swatch sheet my white pens. There's some things in this zipper pocket plus. There's another pouch back here It works really well and again, I can open it flat on the table if I'm out and about with my sketchbook Works and everything I can see everything at a glance, which was kind of the point so I Think that'll work really well And then I can Do that So that works really well then I talked in last week's vlog about the m-grain paint that was like gel-ified and wouldn't come out of the tube and how I broke the tube open and Mixed it in a recycled container with some ox-gallon some water Until I got it blended out and then I was going to just let it dry and have a big like one be one giant big Watercolor pan that you rewet so that's that I'm going to leave the lid off for a couple more days It is an m-grain paint, which I think they're binder's honey. So they never really dry down completely I don't think but We'll see what happens it might See this part is a little bit sticky, but that's probably the honey So I'm going to probably leave it open for a couple more days and we'll see what happens and then the Dusky palette that I made is just about dry And I did add some more pigment to a couple colors. You'll notice if you compare the swatch card Uh from before to now their colors are a little different plus I added one more color Uh Yep, love that can't wait to paint some projects with that the pans are drying some more Anyway, and Things are just a mess up here So I'm waiting for the computer to finish its thing and then I can get all my writing done for the day And then as per usual on Monday, then I have to go do chores So anyway, I think that's it for the minute have anything else planned just chores And random random art projects and I guess getting back to the daughter. It's probably important All right, that's it for right now I'll be back Tell you a little secret my birthday is coming up the daughter wants wants to know what I want to do to celebrate my answer I don't know. I'll let you know what we did, but I have no idea at the moment There's probably just too much going on All right I'll be back. Okay, so I got Stuffed on on the table I have A stack of vintage linens and handkerchiefs some of which are recently purchased some of which I've had for a long time And I don't remember where they all came from but anyway They are ironed as well as they're going to get and at some point this week I think I'm going to be photographing them and turning them into Something more digital that I can print onto paper like this big and then use them in some of my Paper clusters and art journaling. I really like the idea of doing this and I have this collection So I think I'm going to do that There is a couple of etsy sellers that sell digital files of images just like that where they get antique doilies and things and they Scant photograph moments and turn them into or scan them and turn them into digital download I'll try to link one of the stores I've purchased from before down below anyway I also got all of the Written posts for the facebook art groups written Scheduled all the way throughout out through august 1st. And so that is done. I will be probably later This week trying to get Next week's posts written and scheduled also Um ahead of time because Tuesday is my birthday. I don't have to worry about it on my birthday. So like They should be done Monday anyway. Anyway, otherwise, I'm going to do them sunday So I can get the whole weekend done sunday maybe anyway I guess I've been delaying long enough and it's probably time to go downstairs and do the dishes More than likely. I also need to check the mail. So I guess I better get it done. It's not going to do itself All right, I'll be back. Adulting is needed I guess Hello, everybody. I have no idea what time it is. I think it's still morning, but I have honestly no clue If you haven't seen Last week's vlog or the announcement video that came out on thursday last week Then I will link them down below. We should probably watch them But for those who Didn't see that my mother passed away early this morning. It is Tuesday morning july 27th, I think Yeah, anyway, I got a very early phone call from the Hospice per my dad's request and I've spent the morning making phone calls and arrangements and yeah So anyway and the messages are still coming in because of course some people we left always mail for her and It's a lot. So anyway, I'm taking a little bit of a break from live arty chats and That sort of thing Meetings a lot to mail. I guess yesterday's mail finally came at some point yesterday. I don't know Anyway meetings and That sort of thing this week. I will be back hopefully to regular schedule next monday, but The family and I I think need a break and I know I've got to help my dad with a lot of stuff now I'm probably gonna have to drive up there at some point this week and help him clean out closets and All of that stuff so Anyway, my mom was A great supporter of my art journey and this channel and the facebook art groups And all of her children's endeavors even when we didn't get along Very well, but she was always there to support me nonetheless. So anyway All right, that's it for the minute Let me go take care of this And fix my flag, which is crooked again Uh, anyway, it's gonna be hot again today too. So i'm gonna shut up the house and turn the air conditioner on I will be back Wednesday july 28 to 11 o 9 a.m Of course, I've already been on the phone a lot with my dad and other people regarding my mom's passing and all of that anyway I spent some time this morning cleaning out my winter newton pocket box because it was gross And also switching out a few of the colors in here from the originals taking out the white in particular I'd already added three colors across the top, which are a deoxysene purple a panes gray and a black um, and then I Switched out some of the other colors and I added in Um, a pinky magenta color Switched out one of the blues for a more of a turquoisey cerulean Added a very light pale green and this dark forest green. I kept the sap green Um, and I kept the burnt umber, but I added sepia. I think that's a better palette. That's going to work a little better for me um So Yeah, so I did that this morning. I'm going to catch up on some drawing and do some drawing in advance the next few days because of my mom's death are going to be Weird So I'm gonna I have some quiet time this morning. So I'm gonna sit and do that this morning and prep august journals and Stay busy because that's a thing I'll be bounding july 29th. It is 10 29 a.m According to the car clock I am I'm gonna go run some errands I Need to check the p.o. Box because I have absolutely no idea when was the last time it was over there And for those that don't know I do have anxiety disorder issues and When I am stressed Yeah, I have trouble remembering stuff. So Anyway, we're going to go over there first And then I'm going to go to target to pick up a few things in particular. I'm looking for a appropriate blouse Not a t-shirt for the funeral and memorial services I have a funeral skirt fun fact I don't know where my blouse went because I had a up blouse too Um, it may be that it was too small And so I purged it But now I've lost weight. So yeah, anyway, so we're going to go get that done today and then Maybe start some planning for 2022 staying away from Family chats if I can possibly help myself because the family is making me completely crazy And that's a thing. So anyway, all right I'll be back. This whole family of rectoans that come like almost every night They walk seemingly past Definitely past the driveway camera. They seem to walk towards the front door. We can never figure out where they're going We try all the time All the time. Can't find them. Can't find them. They're gone. Tonight's no exception. Good morning, everybody. It's Friday, July 30th It's just after 8 a.m I've got to get my sunglasses hung on See if I can do this without turning the camera off Because I don't know There we go Um, I am so I am Going to go out for a walk Bob's off Running a couple of errands. He needs to run this morning. He has a couple of appointments and um For those that don't know Bob has had a number of skin cancer type moles removed they are actually skin cancer and um He has some more the doctor's pretty sure they're not skin cancer but They do bug Bob. So they're going to remove them any way and test them. So he's off doing that this morning anyway, um I'm going to go out and get some steps in the last two days between everything else that's happened with my mom being ill and passing away and Family stuff that's ensued and it being 5 million degrees again in Oregon Um and hot unusually hot Um, I haven't gotten any steps in not enough in the last couple days. Anyway, I've certainly haven't hit 10,000 in I think three days So i'm going to go get some steps in this morning Because it is going to be at least 99 today if that's what they're expecting if not hotter Which means we probably won't go walking later. So anyway, all the kids are coming over for family dinner night tonight I think we're celebrating my birthday. They all asked what I want. I said to not have to do the dishes. So You know simple things anyway And then tomorrow we're headed up to my dad's to hang out with him for a bit See if he needs anything bring him some food cook barbecue I think we're going to barbecue as a family barbecue and stuff like that. So Yeah Anyway, it's all I can manage right now. I do think that at some point I'm going to do some grief Journally artwork Maybe a brief youtube video or facebook art group video I don't know for sure yet, but if it's something you guys are all interested in leave a comment down below How to deal with like strong emotions in your art It is something I have been doing. I just haven't shown much of it on camera. So Anyway, I'm going to go get some steps in and see what I can see. I'll be back Everybody and I forgot to close the vlog again last night It's been it's been around rough week It's sunday morning august 1st. It's just after nine o'clock. We're headed for a walk Which you'll talk I'll talk about in next week's vlog I hope you guys have had a better week than we have and that you continue to do so And don't forget to have fun creating go for walks Enjoy what you can while you can And uh, I'll see you all next week. Please like share and subscribe If you want to support the free content here on youtube and in the facebook art groups I have a patreon. I have an etsy shop I've got youtube community Sign up for one of them. They're all linked down in the description below summon my link playlist to links Anyway, I'll see you next week go out and have a good one Do something nice for yourself because you deserve it. I'll see you later. Bye guys