Hello everybody hooded cobra commander 788 here and it's time for us to do another vintage vehicle unboxing and assembly It's been a while since we've done one of these and I just felt like doing it So since it's my show, I can do what I feel like doing And we are going to open and assemble this cobra ice snake from 1993 I got this at a very good price at assembly required in Des Moines, Iowa I got it with the attention of assembling it on a video like this. So it's about time we did that. I would not Actually, this this is not a sealed item The box is already torn open. It was like that when I got it. The contents inside are not sealed So we're not really hurting anything by taking this thing out and putting it together I would not open a sealed item if it were from the 80s Those are nowadays just kind of rare and just doesn't seem like the right thing to do to open up a sealed 80s GI Joe item and I wouldn't open up any sealed item from any era if it were something rare But I snakes there are plenty of these around. So I think we're all right here Now when I was looking in this box, I noticed It includes the sticker sheet and the catalog, but it does not include the instruction sheets So I will have to look up the instructions online in order to assemble this But that's all right. Nothing's gonna stop us. I have my tools. I have my glasses. I have my soda Got a Pepsi in here. I'm out of peanuts. So no peanuts in the Pepsi, but that's all right I think we're ready to go. So let's get started. Let's start by taking the contents out of the box and seeing what else here I did peek in here a bit to see If it looked like it was all here, and I think it is Set the box aside for now like most 90s vehicles this came with a cardboard tray inside the box and I believe these parts would normally have been sealed in a plastic bag But as you can see, there's no plastic bag, but the parts are still on the frame So there's that to start with We have the catalog which I did see in there. Oh, and there is the sticker sheet Okay and Catalog this, you know, I'll add this to my catalog collection. I don't think I had this one At least I don't recall having this one so it'll be fun to Take a look through that catalog later And then we have looks like hood and wheel and main body and another wheel and what I assume is an axle and Then a spring-loaded weapon with a black string So I hope that's enough. I'm going to pull up the instructions on the internet and Take a look at this and see what step one is. Okay, slight snag Step one involves a rubber band and there is no rubber band here So fortunately I happen to have a rubber band that I was using for something else So I have no idea if this is the right size, but this is what we've got So this is what we will use.  I need to take this This connector bar off here and we'll get started with that Okay, this dark blue connector bar Needs this rubber band wrapped around it and it's supposed to be wrapped around in a particular way And I've looked at the instructions and I think I get it We are going to try it anyway, at least I hope I get it. I'm gonna do this the way the instructions show I'm not sure I can explain it Okay, this first loop is supposed to go on the hook, but through the second loop and that should Tighten really well Okay, all right. I think I got it, but that's got to be on the hook. Okay. All right.  You have to hook the rubber band on that pull it tight pull wrap the rubber band around The bar and then put the rubber band through that first loop and then put that loop back on the hook So that's pretty tight. I hope this rubber band is large enough to Do what I need to do without breaking, but we're gonna give it a shot the next step if I can Read it here really quick Is we have to put this on On the main body. So here's the main body There's the front Looks like the hook side goes down and the rubber band goes that way and That's supposed to rest in there and the rubber band is supposed to go through this loop in the center Grab that rubber band and pull it through there we go There we go. Okay, so then it pulls through there and it hooks on this post underneath like That okay now so you have a rubber band that runs from this post through this hole out this center post and what looks like the cockpit and wraps around this Dark blue bar, okay, I have no idea what the purpose of that is but It's on there. So let's let's move to the next step and see if we can make sense of this Okay, it looks like we're supposed to take this the roll cage and Essentially put the two ends into this central bar that out of the way like so and then It's supposed to connect which it certainly isn't Connecting very easily. Is there a key to it doesn't look like it. Oh, here we go. Here we go All right, just had to work with it for a second. So now Now the the roll cage is connected to that that crossbar piece with the rubber band on it Still not sure what purpose that serves But it's done. Okay. What next? We're at step five roll cage Lift roll cage and fit wide canopy through the roll cage bars wide canopy fit through the roll cage bars like how Lift roll cage and fit All right. This is going to take a little. Oh I see. I think it fits like this Okay Well, that's not gonna fit very easily All right. Hang on. Give me a minute to look at the instructions again. Okay. All right I think I get it. You have to get kind of get the front end of the the the hood here that Canopy or whatever they call it Inside that roll cage. So yeah, there we go. So that the roll cage bars fit In these notches here. So that's done and then I believe this just Just snaps on We've got a couple tabs on the sides. We've got a tab in the front So in theory, we should be able to just line this up. I Said line it up. Hold on. That's there we go Line it up and press it on until it snaps on so there there There ah success success There we go. All right, so we got the front end assembled the roll cage is on Let's see what the next step is. Okay. I get it now. I get it now step six is just activating the roll cage Okay, so the roll cage you close it by putting these two These two pegs into these two holes, right and that holds pretty well, but it actually has like spikes on it There are spikes on the roll cage and it shows a Graphic here like you have some GI Joe's in front of your I snake here and you want to take them out. You just lift up on that roll cage a bit and bam Instant deadly weapon that is hilarious and I love it. Okay Next is the axle installation upside down guide post on on white axle into White vehicle body as shown This looks like a guide post Looks like it goes that way Press down on axle until a white vehicle tab and post snap into axle slot and hole as Shown, okay, I believe I see it so that goes okay, so this Axle piece it actually fits right over the post that the rubber band is wrapped around so If you align it correctly, it should go yes perfectly like that and then it should snap in Let me see where the tabs are so I can Press it in the right spots so it will snap in but not break Ah there. Oh, yes. Yes. There we go. There you go. Alright, so axle is assembled and next step is Ah the the ski assembly so still got to take the skis off of the frame so Let's do that We go See And there okay, all right, didn't cut the front tips off there And come on come on There, okay. All right, so we got the skis off and these this should be pretty simple let's turn it over and And Match blue skis a and b with white vehicle slots a and b and press into place So I guess they are not interchangeable. So which one ski a Ski B, and it took me a minute to figure out what I was supposed to slot it into but I guess it goes like this and And press in until it connects there we go there we go I Thought it connected to this front sort of area here, but looking at the instructions a little better It connects a little farther back. Oh, that fits really well. Make sure that clicks into place. Yeah All right, we have skis dig it dig it. We have skis now we have skis, but we need wheels So the next is the wheel assembly we have two of those those let's see Snap the two back wheels into onto the white Axle posts as shown That is about as simple as you can get you've got mushroom clips right there the wheel goes on Press on Well, it's not it doesn't go easy does it okay? I want to be careful not to break that so According to the instructions, there's no secret to it. It's just a press on until it stays on So that is that's worrying me right there. That looks like it wants to break All right, that is Seriously not going in There's no left or right wheel I may need to I need to take this wheel off Before you go any further because if I press any harder on that or if I try to twist it It's gonna break that axle off. So hold on time out. Okay. I got the wheel off without Breaking the axle or the wheel but they're like some of the plastic on the wheel has shaved off onto the Post and some of the plastic on the post is left inside the wheel. So this Worrys me. I don't want to have another breakage situation like with the ninja lightning but these wheels are not fitting on well and I Need to figure out a good way to put them on Unfortunately, and so okay. All right. I got one. I think I got one. Yes. Oh, yes It snapped on the instructions. I tried the other wheel on this side and it it seemed to go on a bit better The instructions are no help at all. It just says press it on.  So I Don't see any indication that there's a left and right wheel the wheels look identical But for some reason this one was not going on that side very well So we'll try it on this side try to press it straight and not Not get it all sideways. This wheel is just gonna give me trouble isn't it? All right. Oh There we go. Oh, it's on it didn't break. Oh, oh goody. It didn't break That okay. I don't like that That was much harder than it should have been And I felt like it was gonna break it did It did clip on it didn't break but Yeah, that was much too tight to fit. I feel I think there was a better way to do that All right, pause just for a minute to take another look at the instruction sheet And it looks like we need to put the launcher on next the launcher has a pivot to which it attaches for anyone concerned that I am Using my hobby knife here on the table surface this table surface Was purchased because it is tough and sturdy and it will be just fine It's also usually covered up with poster board for my Refuse I shoot the reviews on this surface So don't worry about it. Guess what? You don't even need to put it in the comments. Everything will be fine So this goes in here and it looks like it goes in firmly Like the wheels they it certainly is a tight fit So I'm gonna have to I don't want to break it But it does it's gonna have to work with me here. It's got to go in It's like that that mushroom clip that on this tiny little pivot is too small For the post that it's supposed to go into All right, I have to work with this Seem to have mislaid my pliers which would have been a big help in this situation I may have to go find them because I'll wait. Hold on Maybe Well, that is tight. Ah, there we go That's on yay and then next Next next next come on And just put this on it. Yeah like that Should just pop right on that little clip right there trying to let you see it a little bit better There is this bar right here that goes on this clip right there at least in theory and Let's see Yeah, it just goes straight on or at least it's supposed to That's another really tight fit And unnecessarily tight fit Why you do this to me Hasbro? Why do you do this? You know this this is supposed to be assembled by kids in 1993 This should not be a struggle for an adult in 2020 All right once again, I've got to be very careful with a part here because this Does not want to give and I need that clip to grab on to this bar And I'm gonna have to negotiate it a bit Okay There okay Again another scary piece to assemble it doesn't look like yeah, it doesn't tilt up very much There because there's a little stopper right there behind it So it doesn't tilt up very much, but it will now pivot And we now have to we have to tie some string here. We have to tie some string to This grapple hook here, so let's go ahead and oops. Let's cut let's cut that off, and I Was looking at the instructions to try to figure out where to tie it on and it took a minute to figure out It says I'm supposed to Tie it to one of these holes in Or on the grapple missile and then the other end is supposed to go on the launcher rings and I Doubt you can see it, but there are a couple really small rings right there where my finger is On this launcher and it looks like it's supposed to go into One of those so we're gonna we're gonna thread it through All right, and then we're gonna tie it We'll knot it a couple of times and that should do The other end. Let's see if we put it in this way this side of the missile. Okay, we're gonna We're just gonna loop it through this hole on the missile and Tie it Tie a couple knots If I can I'm trying to not tie big knots, right? I'm trying to keep the end of the string kind of short without a lot of excess on the end but my fingers are Too fat to really do it right, so we're gonna keep trying This thing is almost done basically we just got to put these other missiles on and Then we got to get to put the stickers on that's always my favorite part man. This string is not cooperating I needed to thread through that loop Like so there we go and tighten Now if I load this thing in the launcher Press it until it clicks. Yes And if I fire it The string should hang on to it here we go Okay, what's going on? That's the trigger There it goes There you go. That was kind of fun. Let's do it one more time Really has to go all the way back and then trigger Okay, cool. All right. Well, I Want to put too much pressure on the string, so I'll just kind of rest it in there for right now I Get back to our instructions. Yeah, so basically Cut these extra missiles off and These are extra missiles that can be used with the missile launcher So Yeah Fire these missiles, but of course one nice thing about At least some of these 90s vehicles that have missile launchers is they gave you a way to store the extra missiles so you get a couple extras and Yeah, they just go in here. I guess How are they supposed to go? They just oh, yeah, okay. Here we go. There. Okay, so wait that should go in further I think there. Okay. All right, so No There I think So we got missiles in front for storage we got I guess I'll just have to Press that in there. All right next we have the stickers Put on the stickers always the best part And unfortunately, I have to do this on my side So you you don't necessarily get to see it until I turn it around but this should be Easy enough. It looks like number four goes right on the side. I like these these are like silvery kind of Reflective stickers. That's kind of cool And we have We have a cobra emblem with like Icicles and a snowflake in the background. I don't know if I want that to be like the cobra Arctic emblem but It's it's different It is different. Okay, so there's that what number is that number five Where's number five? There's number five and number five caution sticker goes and the front the main body looks like on the hood piece and Like other 90s vehicles it is it's instructing me if I'm gonna move it for a little farther back It's instructing me to place stickers over some of the molded details and I don't love that So we got a couple on And what's next number six goes there This number six There's number six number six let's try to Grab that and that goes in this piece over the back wheel like so And I think that's all for that side Looks like it Let's see we got some that go on the top That's the number eight and number eight Let's see That is a classic cobra emblem with a trademark stamp on it Because cobra likes to protect its intellectual properties and this is supposed to be facing The back so this goes on and I don't want to cover this little molded in fuel cap So this should go right in front of it Like So there we go Same on the other side Let's see Well, I'm gonna have to switch hands with that because to get that Okay All right, so this This is my favorite part of the assembly. I really like applying the stickers. It's just it's It's nostalgic and it's just kind of a quiet Activity it's calming Get a bit of Zen for the day All right cobra emblems now we need to put the ice snake Where does that go oh I see the ice snake thing goes there. Oh, and then we have a lift sticker number nine Which goes I don't understand where it's pointing. Oh it goes there number nine sticker goes right so Like so and I'm guessing that the little arrows on the lift sticker face to the front Which would make sense because I think it's supposed to be pointing at the canopy So it would be It would be here Try to center that pretty good best I can anyway Not bad All right, and then this part right here we have this like I Think that's supposed to be like ice snake, but with like with icicles hanging on it it's kind of silly but That's okay The whole thing is kind of silly, but we love it anyway Okay, so this Goes on just like that. Let me try to center this Yeah, it's about the same width as this kind of molding on the hood so that helps center it There Not too bad ice snake We have a stay clear That's number seven That's number seven it goes right there and with the arrow is pointing up So that goes here All right these little caution stickers and stay clear and you know on some vehicles You are no step stickers. I think just adds a bit of verisimilitude to these vehicles although, you know in the 90s they got so wild and Divorced from the from reality. I don't necessarily know why they bothered to to give them any kind of a realistic feel to them But you know, it's all right. It's a nice try Cobra snow Goes there And as much as possible. I am trying to not put these stickers over the molded details It would have been nice if some of these stickers they kind of worked around of the details on the on the toy TPH rescue goes on this side.  All right, I am amazed that anyone actually sits through all of these videos So if you've made it this far, I appreciate it and thank you And let's see There seems to be Yeah, we've got another number six sticker that goes This side is trying to get along got pretty well with where it was on the other side So it will be as symmetrical as we can make it Got one more caution sticker that goes there And we got one more Big Cobra snowflake and that is our last one. I kind of dig these stickers though It's a bit unique having these kind of reflective foil stickers They're kind of cool Dropped a missile off, but I'm trying to line this up with how I added on the other side Yeah, pretty much dead center there Okay, stickers are assembled and there is our Completed ice snake and that was my unboxing of the Cobra ice snake from 1983 I did enjoy it, but although there were some stressful parts to it Some parts didn't want to go on very easily Seems like it's that way with every vehicle we assembled some of you may have noticed that this box is bilingual This looks like a Canadian box Canada got the same vehicles we got in the US But when there was an American flag sticker or a sticker that said USA on it It would be a Canadian flag or it would say Canada instead of USA Well on the Cobra vehicles, you know, you didn't have an American flag So I believe this would have been identical to the US release Except the box also has French on it as well as English So yeah, there you go. I Know this type of video isn't gonna be everybody's cup of tea Not everybody is going to enjoy sitting with me and putting a vehicle together. It's it's not Exciting it's not high energy is kind of low-key, but I enjoy doing them and I'll do them as much as I can So as I get vehicles that are cheap enough and you know, not rare That we can assemble I'll do more videos like this, but mainly I'm working on reviews I'm actually in the process of getting some reviews ready right now. Just thought I'd take a break from it I hope you like what we have coming up but Just remember New video goes up on Sunday And every once in a while in the middle of the week. I'll give you something like this So thanks everyone for watching. I'll see you soon with the full vintage GI Joe toy review until then remember only GI Joe is GI Joe


The city of Bemidji is making some changes in 2019 when it comes to its public spaces. The city council held the first reading of its new special events ordinance this week, which coincides with the rollout of a new online park reservation form. The online program is designed to expedite the reservation process with less paperwork. It's also designed to provide everyone with the same guidelines when holding an event in a public space. We want to ensure we're protecting our resources. So when you're talking about where we have Lake Bemidji, we have people resources, we have you know our parks, what do we do with food vendors and ensuring that you know any sort of grease, where is that going as such and be going into our lake? So is there a process for that? How do you remove the garbage and making sure events have plans for those? So these things are also taken care of and we're being good stewards of our environment. The new online reservation forms are now live on the city of Bemidji's website. The city will hold its second reading of the special events ordinance at its next council meeting. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


Welcome back everyone in this video. We're gonna start doing some calculus with polar functions That is functions of the form r equals f of theta and frankly speaking a lot of the calculus is gonna be based upon the fact That we can view polar functions as parametric functions And how one does that comes from what we discussed before We had seen previously that as we switch from Polar coordinates to Cartesian coordinates we get the following r equals r I'm sorry x equals r cosine theta and y equals r sine theta Well since r is itself a function of theta we could insert for r f of theta Like we do right here, and so we get x equals f of theta times cosine of theta and y equals f of theta times sine of theta And so that way we can view polar functions as Parametric equations associated to the parameter theta And so the reason why this is an important perspective is that as we want to talk about tangent lines of a polar curve The tangent line will still be determined by this rise over run We're looking the slope of the tangent line will still be dy over dx and so we have to express dy over dx knowing how r is a function of theta So if y and x are both functions of theta You can replace dy with dy over d theta and dx with dx over d theta by the chain rule that these two quotients will still be the same thing and if you take the derivative of Why I guess we'll do why first if you take the derivative of y with respect to theta first using the Product rule you're going to get r prime and by r prime here This will always mean r prime always mean dr over d theta and Theta prime will always mean dy over dx if we ever abbreviate that we won't deviate from those So taking the derivative of y with respect to theta remember f of theta is just r here So by the product rule you're going to get the derivative You'll get the derivative of r first times sine theta then you're going to get r times the derivative of sine theta Which is cosine Taking the derivative of x with respect to theta you're going to get r prime Cosine and then you're going to get negative r times sine theta the derivative of cosine is a negative sign and So we can actually get the derivative here And so this is a form of one can Memorize but really these yellow boxes right here is what you want to know that x equals r cosine theta y equals r sine theta And since r is a function of theta you can take the derivative with respect to theta on top and bottom And that's going to help us out here So let's do a little bit of analysis of a Corioid take the function r equals 1 plus sine of theta and let's look at some tangent lines for this curve For example, let's find the tangent line When theta equals pi thirds Well, let's focus on the slope. We can do the rest of it if we want to now pi thirds be aware it's going to be It's gonna be about this angle right here And so the tangent line we can kind of visualize would be something like this thing right here If ever you miss your dot just draw the dot bigger so you get to become the tangent line So this is roughly speaking what we're looking for we need to find the slope of this line So what we're looking for is we're trying to find y prime like we saw before is dy over d theta divided by dx over d theta and So be aware that we're going to be getting r which is 1 plus sine theta times that by sine We need to take the derivative of this on top and then we have to do the same thing for x.   Sorry another another sine theta cosine theta So I'm just gonna put a 2 in front right there In the denominator What we end up with we're gonna get a cosine times cosine so a cosine squared When you distribute you're gonna get one on the sign, so it's gonna be a negative sign and Then when you get sine and sine that's gonna be a negative sine squared Like so and so to try to make this thing a little bit simpler I'm gonna want to utilize some trig identities notice that 2 sine theta cosine theta That's the that's half of the double angle identity so we can end up with sine of 2 theta plus cosine and Then this it's above well actually kind of kind of works out nicely here cosine squared minus sine squared That's half of the double angle identity for cosine you end up with a cosine of 2 theta Minus sine theta so there's some symmetry to there. So this right here is just the derivative y prime, right? We next need to calculate. What is the derivative when it's evaluated at? Theta equals pi thirds Now it's the angle of consideration. So plug in all of these appropriate parts in there. You're gonna get sine of 2 pi thirds Plus cosine of pi thirds This sits above cosine of 2 pi thirds Minus sine of pi thirds If it helps of course pi thirds Would be 60 degrees 2 pi thirds would be 120 degrees now 2 pi thirds references to pi thirds It's just in the second quadrant now sine and the second quadrant is identical Just the angle doesn't make a difference. So you just get the first one right here. You could replace You could just replace it with a sine of pi thirds. It would be the exact same thing And so sine of pi thirds is gonna be root 3 over 2 Or adding to that cosine of pi thirds, which is one half in the denominator We're gonna get cosine of 2 pi thirds which 2 pi thirds It references pi thirds, but for cosine that I'll actually make it negative. So you're gonna get a Negative one half in the denominator minus pi thirds Which is going to give you the square root of 3 over 2 So despite as complicated this might look notice in the bottom in the top and bottom you get 3 over 2 Plus one half factor out the negative sign You're gonna get 3 over 2 plus one half This will simplify just to be a negative one and that's then the slope of This line that we had above here And you know if you look at that line as we drew it It's not perfectly drawn to scale, but negative one actually does seem to be a about a Slope of that tangent line. So I feel like our calculation worked out really well so another thing to consider is Where are the horizontal and Vertical tangent lines of this graph and on the picture we can see them There's looks like there's a horizontal right there at pi halves. There's gonna be two horizontals In the third and fourth quadrants. We'll have to come back and figure out those are there's gonna be two vertical tangent lines in the first and Second quadrant and then also we're gonna see that this cusp here at 3 pi thirds is gonna be kind of suspicious For our derivative here when we investigate it So let's find these points for where the tangent line is vertical or horizontal coming back to our formula, right? dy over dx Remember this was sine of 2 theta plus cosine theta Over cosine of 2 theta minus sine of theta. That's what we saw on the previous slide Did we not I think we did Let me just double-check. What was it? Yep. That's what we had So we want to figure out when this thing is horizontal that when the tangent line is gonna be horizontal and vertical so just as sort of a quick reminder here the The tangent line is gonna be a horizontal tangent line when we get that our dy is Zero, but dx is not zero and the vertical tangent lines are gonna correspond when the dy is not zero But the dx is zero now Of course if they both are zero at the same time you have the indeterminate form zero over zero And you might need low p-tolls rule to help us determine what's going on there All right, and so let's start off with the horizontal Well, let's actually solve all these things when they're equal to zero, right? Sine of 2 theta plus cosine of theta when this is equal to zero It'll probably be better to go back Sine of 2 theta will replace with 2 sine theta cosine theta I think the calculation will be a little bit easier when all of the angles are the same You notice you can factor out a cosine theta from this that leaves behind 2 sine theta plus 1 and So by the zero product property this implies that cosine theta equals zero or That 2 sine theta plus 1 equals zero so for cosine Cosine is equal to zero This will happen at the top of the unit circle and at the bottom of the unit circle So we're looking at pi halves and 3 pi halves and of course angles which are coterminal to those ones Now for 2 sine theta plus 1 if we solve for sine here, you can subtract 1 divide by 2 We're trying to solve the equation when does sine theta equal negative one half now We do know a 30-degree angle sine is equal to one half or that is sine at pi 6th will give us a one Sorry a sine of pi 6 will give us a one half so using reference angles that can help us out a lot here We are gonna get that theta Would since if sine is negative It's gonna be in the third quadrant or the fourth quadrant, but it should reference to pi 6th now That's gonna be exactly 7 pi 6th and 11 pi 6 now admittedly there are angles coterminal to that but As the whole cardioid is graphed by from 0 to 2 pi. We only have to find theta between 0 and 2 pi here So this tells us when the denominator when the numerator goes to 0 here on in contrast When does the denominator go to 0 cosine of 2 theta? minus sine theta is equal to 0 Likewise, we want to put you know, we want to compare apples to apples We need to have theta and theta not a 2 theta here So we could switch cosine of 2 theta back to cosine squared minus sine squared But I actually think a different Trigonometric identity would be useful here, right? So we could also use the fact That cosine of 2 theta. Oh boy. Let's see if I can remember it We we we use this identity all the time for trigonometric identities If you don't remember it, we'll just just kind of do this cosine squared minus sine squared Right here minus sine Now because of the pythagorean identity, we do know that cosine squared theta minus or plus sine squared theta Equals one if you solve for cosine squared here, you're going to get cosine squared equal to 1 minus sine squared So just make that substitution 1 minus sine squared In which case you end up with 1 minus 2 sine squared theta minus sine So what you kind of see right here It's just want to point out that if you don't remember a trig identity Your your first goal doesn't always have to be go look it up You can often derive them from the trig identities. You do know here.  So that combines to give you a single sign So there's reverse foil going on there kind of skip some of the details. I hope that's okay with everyone Uh, and so which case if we continue with this, we're going to get 1 plus sine theta equals 0 Or we get 1 minus 2 sine theta Equal 0. So now for the first one Sine theta equals negative 1 when is sine equal to negative 1 that happens at the bottom of the hour That is the bottom of the unit circle that'll happen at 3 pi halves And then for the other one if we solve for sine we're looking for when sine theta equals 1 half And like we said before that'll happen at pi 6th But also whenever sine is positive it references to pi 6th, which would also happen at 5 pi 6th So we see that the numerator of the derivative will be 0 At pi halves 3 pi halves 7 pi 6 and 11 pi 6 It'll be The denominator will be 0 at 3 pi halves pi 6 and 5 pi 6th And you'll notice here that There is a little bit of overlap 3 pi halves shows up in both situations We're going to have to investigate this one a little bit further because in this situation our derivative dy over dx Looks like 0 over 0 If we go back to the picture That we saw before this actually might agree with what we were looking at right So when does when does the when does the numerator go to 0? Pi halves that's the top of the circle at the top of the cardioid and then at 7 pi 6 and 11 pi 6 So what we're seeing right here Is this one happens at pi halves? This one right here. It's happening at 7 pi 6th And this one right here is happening at 11 pi 6 just like we calculated In terms of vertical tangent lines well 3 pi halves will come back to that one You have pi 6 and 5 pi 6th. So we can see that for these ones The vertical tangent on the right happens at pi 6th And the one on the left happens at 5 pi 6th And so by symmetry those all seem to match up right And so the suspicious thing that's left over is at 3 pi halves, right? That's where the cusp is on our cardioid So it's not surprising that 3 pi halves gives you this indeterminate form Funky things are happening at 3 pi halves for our cardioid so What we've seen so far is that dy over dx You're getting this indeterminate form. So we're going to apply l'Hopital's rule in this context We're going to take the derivative of the top and bottom yet again. So if we take Sine of 2 theta plus cosine theta We're going to take the derivative that again with respect to theta for the bottom. We have cosine of 2 theta That is a 2 minus sine theta Take again the derivative with respect to theta Because that's how we try to resolve this indeterminate form using l'Hopital's rule So l'Hopital's rule will give us 2 cosine 2 theta minus sine theta And then on the denominator, we're going to get negative 2 sine of 2 theta minus cosine theta Like so and so then Continuing on from there if we were to plug in 3 pi halves because we really only care about this thing as theta As theta is approaching 3 pi halves. So let's try that this time around You would get 2 cosine of 3 pi. I like that minus sine of 3 pi halves And then in the denominator, we're going to get negative 2 sine of 3 pi minus cosine of 3 pi halves So now we have the battle the clash of the titans who's stronger numerator denominator who wants to win this fight So going through this some things to note Cosine of 3 pi is the same thing as cosine of pi. That's going to be a negative 1 Sine of 3 pi is going to be a 0 Sine of negative Sine of 3 pi over 2 that's going to also be a negative 1 And then cosine of 3 pi over 2 that's going to be a 0 So you can see what happens here is in the numerator We end up with negative 2 plus 1 The denominator we're going to end up with 0 plus 0 So looks like we end up with like a negative 1 over 0. Assuming we didn't make any mistakes along the way But this seems to say that the winner winner is the denominator here So this thing wants to be a vertical tangent line A vertical tangent And if we come back to the picture of the carbioid that does seem to agree with what we were seeing right there, right? As this thing bends upward and bends upward This cusp is coming to a sharp point and thus having this vertical tangent that sits in between them So we can analyze Polar functions using the same type of tangent line consideration we had in the past Just make sure that we take the derivative that you are taking the derivative Treating the polar function as a parametric function Then we can use derivatives and tangent lines to measure things about monotonicity We could do the second derivative measure things about concavity and all of that business For these polar functions, just like other functions as well. And so that brings us to the end of lecture 33 Where we talked about some polar derivatives here in the next video for polar or for lecture 34 We're going to talk about uh, how integrals are affected when we start looking at polar functions. So stay tuned for that one


So I can't believe I even need to have this conversation, but I got to remember that we might have some younger viewers or we might have people who aren't as experienced with social media and the internet as I am. We have something happening on our channel that it's actually happened to quite a few channels. Actually what's happening is extremely popular on TikTok and Snapchat, but some people you know if you're on TikTok you don't really read the comments or comment yourself so you don't deal with this or see it. I know personally I don't think I've ever commented on a TikTok video. Most I've done is ever leave a heart. So yeah you know it's not something I've experienced but I've seen other people that I know use TikTok experience this and now it's happening on YouTube and it's something that I can't really do much to prevent. I do my best. I've been doing my best the last couple days to combat it and help protect you guys. But unfortunately because we especially do things like giveaways we actually have a giveaway going on right now for Switch OLED PlayStation 5 and Xbox Series X winner of choice you know winner gets to choose whatever system they want. Lean.io link down in the description. But the reason I wanted to bring that up is because our giveaways are probably why this channel is targeted because it makes our viewer base just frankly more gullible and I don't want to blame anyone specifically but I have gotten dozens of emails and DMs across social media about this and people who have fallen for it. And what am I talking about? Well here's just one example I happened to screenshot. I delete a lot of this stuff and it says thanks for watching. Don't forget to hit that subscription bell and then it gives a whatsapp phone number. And this username in particular I've actually seen seven different ones. This one uses my thumbnail and then says pinned by Nintendo Prime and that's actually their username but they're doing that to trick people into thinking it's actually me responding to them.  They can only respond it seems per bot that's doing this. They can only respond to about 70 comments per video. And right now YouTube is not doing anything to combat it. They are aware that this is happening, that this is the latest scam happening. And that's actually a nicer one where the bots asking you to subscribe but then also asking you to talk to them on whatsapp. And some people are gullible enough to believe I am handing out a publicly available whatsapp number so people can talk to me. Now they won't actually call you and talk to you so you can obviously figure out hey that's not Nate that's not his voice. What they're doing instead is just texting and yeah telling you that you've won giveaways and asking for shipping details and saying that hey you have to pay for shipping which for some of my giveaways you do have to pay for shipping so it can sound extremely believable. But I can tell you right now I've never once used whatsapp to handle any of my giveaways and I would never tell anyone to contact me on whatsapp. In fact I don't even have a whatsapp number at least not a public one. I have one whatsapp phone number that's private because we have certain sponsors that like to talk through whatsapp for some ungodly reason but we personally don't use whatsapp in any public capacity. So I can tell you right now anytime you see a comment responding to the tone that you've won contact me on whatsapp or oh subscribe thanks very much by the way contact me on whatsapp all they're trying to do is fish you get your address your phone number so they can send spam calls and spam mail to your house and also so they can try to convince you to send them shipping money which they are obviously just going to keep and the more you interact with these whatsapp phone numbers the more and more they're going to keep coming after us. The best thing you can do is report that comment right report it as spam and hope that YouTube's automatic AI starts to recognize that these comments with whatsapp numbers are bullshit. They're obviously impersonating me and making it as believable as they can without being my account and unfortunately because I'm not a channel with 100,000 subscribers I don't have a check mark by my name which would be a way to verify it and gosh knows the bot makers will eventually figure out we have a nintendo prime podcast channel and then start to make bots that use that to act like I'm talking to you guys with the podcast channel which happens now and then depending on what account I happen to be logged in you guys do know I do respond directly to comments here and there I don't respond to everybody because I just don't have that kind of time but frankly and I have to say this and I know it's going to sound mean I've had what a half dozen people tell me um that they think I scam them or that this is a scam and they're requesting that I give them their money back one person in particular requested over $300 that they sent um supposedly so I would ship them to PlayStation 5's that they won in a different country um I've only ever given away one PlayStation 5 that was back in January of last year now obviously we might be giving away another one this month but yeah to that I can only say I'm really sorry you got scammed but it's not my problem you for lack of a better word I won't name any names kind of an idiot these scam things have existed for a long time whether it's phishing emails whether it's you know weird text messages you know you get phone calls from from companies pretending they're collection agencies and they're not really collection agencies you get a whole bunch of this stuff happening to you throughout your life whether you're a teenager a child or an adult and you have to learn and self-teach yourself to recognize the difference anything that says pinned by nintendo prime is not me there is one pinned comment and that is usually my comment advertising giveaways or asking people to subscribe so every now and then I'll pin a fan comment but yeah I this is really out of my purview it is not on me to refund money that you got scammed out of because you followed a scam that happened in my comment section that youtube unfortunately didn't do a better job protecting now this is something I've seen other youtubers talk about over the last couple of months and they've suggested something that youtube could offer in the meantime that I would really prefer until they could deal with this and that would be the ability to turn off replies they aren't making a normal comment they're replying to people to make it look more direct and harder for me to track and take care of because while I try to read every comment reality is I make multiple videos sometimes five to ten videos per week plus live streams I'm not going to be able to catch everything I try really hard to but I'm not always going to catch it I'm not always going to catch it in the moment I could be doing other things with my children my fiance school etc and I'm not going to get to it and unfortunately that leads to a lot of you guys potentially getting scammed so I'm making this video as a general warning it should be obvious I am not ever telling anybody to go to WhatsApp just to chat with me we have a public discord server everybody a public discord server if I'm going to tell you to go anywhere to talk it will be there I don't hand out my phone number I don't hand out a whatsapp number my twitter my publicly available email and our public discord server that's it I don't have a special snapchat for you guys or a special facebook group you can join I don't have you know I am on instagram and tiktok but I don't tell people to really go there to DM me and talk to me so guys stop letting yourself get scammed and be smarter and I'm really sorry this is happening and I don't want to say it's your fault for falling for the scam but I do want to say I really make people aware of it and no I'm not the one doing it and I have no control over it and no I'm not going to be giving you your money back if you get scammed okay it's not my responsibility to do that all I can do is tell you I'm deeply sorry that this happened and obviously use it as a learning experience to make people aware that this is the thing going on on my channel and it's happening all across youtube by the way it's a very widespread problem and now that it's starting to get down to smaller content creators like me I can only imagine how many of the other channels you watch whether it's rgt swanwave andres restart etc that's going to end up dealing with this problem as well so please don't be dumb don't let it happen to you so the only time I'm going to warn you about it because it's out of my control and has nothing to do with me all right folks I'm Nathaniel Ruppeljantz from Nintendo Prime and hopefully I'll catch you in a much more upbeat video next time


So my vision for the 19th Airlift Wing as we move out together is that we build courageous leaders, that we develop mobility warriors, and we nurture a connected community. You'll hear me talk about that a lot, courageous leaders, mobility warriors, and a connected community. Because at the end of the day, that's what it means to be Black Knight. We are courageous leaders, which means we are bold. We embrace failure, and we learn and grow through failure. And that's what being a leader is about, is taking that bold step. Mobility warriors, this is something that we've been doing already. So we're building on what we've already started, and the Black Knights have already done that. So we're really proud of the work that's already been set, and we'll continue to grow on that foundation. And then lastly, we need to have a connected community. I want every airman, every family member, everybody that lives and works and plays on Little Rock Air Force Base to feel that they come from a community that knows them, that loves them, where they feel that they belong, and they can reach their fullest potential.  We need to be ready to deliver air power anytime, anywhere. So if we can do those three things, we can get after that part of the mission that our nation is counting on us for.