Welcome to Access to Trader, the number one community for those who are committed to taking control of their trading in order to achieve success, profitability, and longevity. Thank you for joining us. Here's Dan Shapiro to help you find your edge, master your process, and own your future. Hey guys, good evening everybody. Happy Monday and welcome to another edition of the AccessToTrader.com nightly update show. Hope everybody a great weekend. Hope everybody enjoyed the Super Bowl. Hopefully your team that you were pulling for won. And now football is over. Let us all pray again. It's a dark time and so preseason again. So let's talk about the tape. Most important developments going into today's session. How were the equity markets, especially the NASDAQ composite, were going to react to last week being the first week that we took a step back, right? I think that was the most important part. Two and a half percent breather on the NASDAQ last week, which wasn't a big deal considering again the NASDAQ was up as much as 17% at one point last week. And the question is, what was going to happen ahead of the CPI? Tomorrow obviously is the biggest reading of the week. Tomorrow is the February CPI, the consensus around 6.2 or so, right? 6.2. The question is, how is the market going to react? I think based on what we saw today's action, there's two thoughts of reason. One, a nice little bump up today. Very, very choppy in the first couple of hours. I came in today, if you watched the video last night, I came in today. I was looking for all my data was telling me we were going to get another day of a potential back to. So I was looking for another sell-off that obviously never came today, but no harm, no foul, nothing confirmed. But the point is, and everything just started dripping, like literally it was like a slow drip, but to the upside. And for every stock that was very strong today, and you can make an argument, Microsoft definitely led the way, continues its wave on the AR charge. But you had Apple, you had Apple wake up today very, very strongly. You had Meta today very, very strong. Again, it's not going to really show or demonstrate, but what Meta is doing right now, it's one day away from confirming the 5-day moving average. Even Netflix, they came out with some pretty aggressive put-buying right off the word go, right at the open. It deflected it very, very clean, and now it's a day away from reclaiming the 10-day moving average. And going into tomorrow's session, luckily we don't have to wait until like 2 o'clock, 2.30, the same as the Fed. CPI comes out tomorrow at 8.30. The problem with the CPI coming out at 8.30 is it's very, very tough based on the last 6-7 CPIs that came out. It's very, very tough to get a game plan from one side of the market, right? We've been seeing 3% moves, 4% moves, 2% moves, 3% candles, 4% candles in either direction. So to go in and make yourself an actionable trading plan for tomorrow with only one side of the market is going to be a very, very big problem. Because again, you could take a look at the market and go, oh, cues, cues look great, right? Look what they did today. Cues had a pullback of 2.5%. They rebounded today. They reclaimed the 5- and the 10-day moving average super bullish, right? Markets should go higher. Well, again, that's the whole point of the CPI coming out. We don't know what's going to happen because the whole argument is, well, today's little 1.5% meltup on the NASDAQ 100 is kind of priced into tomorrow's move. I mean, how we possibly even pretend to even know that or pretending to guess, we don't know. And the point is if I'm turning around and saying to myself, well, I think the cues look great above today's price action. Yeah, that's great. But if the CPI comes out and the data is well received, we're not having the conversation down here. We're having the conversation up here or up here or even down here below the previous range. So it's very, very tough. And I think a lot of you guys are going to realize, unless we get a very muted reaction, the biggest problem going into tomorrow's session, once the CPI is released, you're going to have a pretty big move, right? Pretty big move in either direction, which is going to negate a lot of channels very, very quickly. And unless you're one of these, shoot first, ask questions later, and don't let the market to kind of simmer a little bit, don't let the noise digest or digest the information, you might get caught. Maybe get lucky off the first move of the CPI, but there's a good chance if you are unlucky. And unfortunately, luck does play a part of it. But if you're unlucky and not patient to let that first move to kind of simmer, to kind of play out a little bit, you can have a very, very aggressive start to the day. And that's our biggest issue tomorrow. The market perceives this number as good. You might be buying stocks well above the previous, today's range, well above the previous day's range. That's called, you know, you're putting in your position to chase, right? And the same thing to the downside. So I tried to do my best today, well, at least this evening, to kind of give us an opportunity to kind of trade both sides of the market. So for example, and again, you want to, when you're talking about stocks trading both sides of the market, you want to use, you know, stocks with the biggest average true range. What's the biggest two average true range stocks, especially in 2023? Well, the first one is NVIDIA, right? Look at NVIDIA. NVIDIA had this massive run. If you look at the range today, it had an upside of 220, right? 220 in change. You had a downside of 209. So you're talking about, what, 11, 12 points of average true range. So you can see here, here's a definitive stock that has a perfect scenario, right? An absolute perfect scenario for the top of the range preparation and the bottom of the range preparation. Something's going to give here, right? So I tried to make a watch list tonight, you know, of names that I think that despite a potential big move and who knows which direction that we give us ourselves a fighting chance technically that we don't have to chase, right? That's the whole point, that we don't have to chase. We don't have to anticipate the potential next move because there is so much violent average true range. So even if NVIDIA gaps up above the previous two days range, look at which room you still have to go, right? You still have room from the bottom channel here on February the 9th to all the way the highs of 230. So there's a lot of room here and the same thing to the downside. As you can see here, it held the bottom of the range here back to back days. So if the number is perceived bad, you still have, what, 10 points, right? You have about 8 to 10 points of downward bias as well. Same name, for example, like a Tesla, right? You know, Tesla has been on a phenomenal run the last couple of days. Some pretty aggressive, you know, some pretty aggressive pullback. You know, again, we pulled back from 214 all the way down to 187 in three days. That's not a small thing. Again, the Contra argument is, well, that's not really anything considering the stock since January the 6th has gone absolutely berserk and has gone from 101 to 214. To Shay, right? To Shay. So the key is for Tesla, for example, you have to use the previous days range, right? So not even today's range, you've got to use the previous range and obviously today's lows. Because again, one of those channels will confirm when the price action starts to expand. The problem is if you're not trading beta, right? If you're not trading beta, you're not going to have the same type of scenario that, for example, myself is going to have because again, I trade beta stocks. I trade the stocks with the biggest average range. So for example, if you're trading a smaller name, right? A smaller name, like a FSLY, right? I'll give you an example. Like FSLY had a really, really big move today. Huge expansion, right? Absolutely huge expansion. Had a beautiful day and stopped at the top of the channel here. So if this starts confirming, well, at least you wanted to confirm today's channel, you're not going to get the same type of average range that you got today. It's right? What's one of those scenarios that's an outlier of what the stock normally does. So you're going to be, you know, in a weird way, you're going to be bidding up a stock above today's range, not knowing what the true average, true range of the stock truly is. And maybe paying 50 cents, 60 cents higher above today's range could be a very, very big problem versus paying a couple of dollars above in the video's previous day's range could still give you 8 to 10 dollars depending how aggressive the market is. So tomorrow is going to be a little bit of a tricky day, right? A very, very tricky day. I think a lot of traders already have it in their mind that today's session is kind of a sneak preview that people had, maybe the number, somebody got the number, leaked the number ahead of them. It's possible, right? Everything's possible ahead of time. But the most important part is even if you have, right? Even if you have the CPI numbers right in front of you, we never, absolutely never know when the market or how the market is going to react. So the only thing we can do is, and this is my advice, especially for all you guys who trade, who trade technology names, take the stocks that you do trade, right? See where the previous channel is to the upside, right? Like we talked about right now on the video. And see where the previous downside channel is. And make your feasibility study, right? Based on where the stock is going to trade and confirm. Not today's range, but the previous day's range. I think that's the only high probability that we have. And ironically, it's one of those scenarios that you can't play the first dip. You can't play the first rejection because you really don't know if it's a truly trend day. You're only guessing, you're only anticipating. So anytime you have days that are Fed driven, Fed notes, POW testimony or CPI or PPI. Remember, those days are the most absolutely aggressive, right? Absolutely aggressive days.  It's going to force you to put yourself in a position that you're uncomfortable. You're trying to chase the price action that might not be there. Because again, in your mind, you don't want to miss it, right? The whole fear of missing out. So be careful tomorrow, right? In a weird way, I'm almost hoping for, if you believe this closes good, and I do, right? I do believe this closes good. I think the fact that we close above the 10 and the 5-day moving average on the Qs, at least it's giving us a glimpse. If nothing was on the docket tomorrow, then this would be a really positive close. But I think the best thing the market can do is actually have the first reaction to be negative. Because if you guys do remember the last couple of times that we had negative initial reaction, whether it was the CPI or whether it was Powell's testimony, remember that Powell's testimony two Wednesdays ago after the Fed minutes, right? The initial move was down, and then it was up, and then it was down. And then the third time, right, through the previous range, that's when it confirmed we had a really violent move towards the end of the day. I think it'll be at least a lot safer than buying, for example, up Microsoft, up 11, knowing that the previous range is only $2 away. So we want to stay safe.  Again, if you watched my video two Wednesdays ago ahead of the Fed, right, ahead of the Fed announcement, I said the same thing. I think a lot of new traders are always putting themselves or putting the next trading day that's supposed to be kind of a big deal, a big event, way up here, right? They're sensationalizing the day, and right away they go into the next trading day with these incredible, incredible visions of what they think is going to happen or potentially is going to happen. And unfortunately, because of the violent nature of that event, yeah, you might be right, but the problem is you might get faked out 68 times before that. So you want to stay with days that are controllable, that are lethargic, that are predictable based on the previous night's close. When you're going into an event, again, and this is the unfortunate part, a lot of new traders are already hyping this day up tomorrow in their heads. They think there's going to be a 900-point rally, the other side of the trade thing is going to be a 900-point sell-off. You've got the AI, remember that the AI predictor that the market's going to crash the next day? Well, we'll see about that as well. But the point is, again, don't sensationalize a trading day. There's going to be thousands and thousands of trades ahead of you, thousands and thousands of hopefully days ahead of you. This is just one normal one. So going into tomorrow's session, just take a deep breath, right? You don't need to catch every single trade. You don't have to be in every single move. You don't have to be in every single interview. You don't have to be in every single channel. If you don't want to trade, don't trade. Okay, and always think longevity, guys. Think of the long game. Will I be on alert for both sides of the channels? Absolutely. I'm watching the video. I'm watching Tesla. I'm watching AMD, right? These stocks look great. I'm watching Meta, right? In case the number is good and the initial reaction is going through bad. Again, I'm watching these things off of today's range, but we have to have a contingency plan. In case they gap up aggressively or gap down aggressively, we want to use the previous day's range, right? The previous day's range as an area that if the market does go in that direction that we are prepared. So Meta I like, and the video I like, Tesla I like. And in case the market starts pooping out as well, look at Google, right? Google really didn't rally today. It's hanging on that 50-day moving average like it's grim death, man. So we have to be prepared. Again, we have to be prepared every single day, but now we have a little bit more of extraordinary circumstances. And again, if you're a brand new trader, again, do not trade pre-market. You'll get chopped up. Do not trade anticipation. You'll get chopped up. Do not trade if you feel your heart palpitating out of control, even though there's really nothing that of a big deal that is happening is. So if you have all these things and you're hyping up the day, you're probably going to find yourself in a very, very dark place tomorrow. And not just financial or very mentally and unfortunately a lot of new traders, they just can't get over that hurdle. So running into violence is definitely not going to help. Unfortunately today, I just kind of sat out the day. There was a couple of pivots. I was, you know, I was sitting there watching the downside that never confirmed. On the video, there was a nice little pivot there. Meadow was a nice little pivot there. Other than that, it was, you know, pretty quiet, slow meltup day. We missed a bounce in Microsoft that was very, very strong. At least I missed it. So kind of a, as the kids say, a nothing burger for me. But again, it's okay. Right.  So that's it, guys. So everybody, I wish you guys lots of luck tomorrow. Again, Rick, stay calm. Take a deep breath. It's really not that serious. Just one trade, one day out of many, and it's just business as usual. Guys, God bless, and I will see you all tomorrow. Take care.


event called the Freakness. That's a tough one. I do not know the answer to that and I have spent my whole life coming to Freakness. I don't know I've only been coming for 13 years. Come over here I couldn't answer that. No clue. I have no idea. I know it was named that over a hundred and twenty years ago. It's named after famous gentleman who was betting on games. I've done no research. It's called the Freakness because we're Freak nasty with all of our outfits. I hate to admit but I don't know the answer to that and I should know that because it was called the Freakness but trademark infringement on the original Freakness which was this crazy party up on King Cod that I can't really tell you what happens there because it was a little too freaky so they just put a line of join the F and made a Freakness. One of the horses early on was called the Freakness. I have no idea. There you go. That's right. Is that right? A horse named Freakness won the dinner steaks party in Pemlico Race Tracks first year ever 1870 name after him and the name has lived on the more you know.


A warm welcome to the 23rd session of the second module of the course signals and systems. We are now in a position in this module where we can deal with more general signals from the point of view of decomposition into sinusoidal frequency components and analysis as to what happens when you pass through a linear shift invariant system. To do that we should try and recapitulate some of the important conclusions that we had drawn in the previous session which will now help us in generalization. So let us look at some of the important conclusions that we had drawn. What we had seen is that if we have a linear shift invariant system let us call it S with impulse response h t and to it we give a periodic input, a periodic signal input, periodic with period t and of course let us assume that the Dirichlet conditions are obeyed that is not demanding too much so we could decompose this into its Fourier series. Now the output can also be written as a Fourier series and the interesting thing is the output has a quantity that depends on the impulse response which I am now writing down here. This is the quantity that depends on the impulse response and in fact we know what that quantity is. The quantity is obtained like this. Now we need to look a little more carefully at what this quantity is and what interpretation we can give it. We had kind of started in the previous session to give an interpretation but we now need to complete that job and in fact then to take it to the input as well if the input is not periodic. So let us interpret this quantity. So if you look at the quantity capital H of omega integral for minus to plus infinity h t e raised to power minus j omega t dt we can clearly interpret this as a dot product or inner product. It is an inner product between impulse response h t and the rotating phasor e raised to power j omega. Now this interpretation makes a lot of sense. Now what does an inner product do? An inner product calculates a projection or a component. So it is as if you are trying to find the component of the impulse response along a rotating phasor rotating with an angular velocity capital omega and at the specific values of omega given by each of the Fourier series components you evaluate this dot product and use it to modify the Fourier series coefficients. Let us write that down formally. Let us focus our attention on how those Fourier series coefficients are modified in going from input to output then we will be clear what is happening in fact the interpretation is very simple. So the output Fourier series coefficients are Ck times h 2 pi by t times k essentially you have substituted the value of capital omega here. So it is essentially the product is the input Fourier series coefficient at that frequency multiplied by the component of the impulse response at the angular frequency of frequencies corresponding to those coefficients. So it is essentially as if you are taking component by component and multiplying by the corresponding component of the impulse response, component of the input multiplied by component of the impulse response, simple enough. Now let us look at how you calculated the input Fourier series coefficients. There was also an inner product there. In fact we do not need to go through the whole derivation again. You will recall that in the input the Fourier series coefficients were calculated by taking an inner product but remembering that you need to take only one period of the input. You took only one period of the input and found the inner product with the corresponding harmonic or the complex exponential rotating with that particular multiple of the fundamental frequency. So here we assume the input was periodic. What if it is not? Can we generalize this is a question that we need to answer. If we look at this quantity which we will now write down very clearly, can we think of this quantity h omega as a new transform or a new way of doing things with the impulse response in its own right? So let us answer that question. So let us look at the quantity in detail once again. Now we have h omega is minus to plus infinity ht e raised to the power minus j omega t dt and this is a function of angular frequency. Now this quantity will be called the name just like we called the decomposition of a periodic function into its sinusoidal components as the Fourier series decomposition of the function. Remember I told you Fourier is the name of a very well respected mathematician. You could call him a mathematician or a researcher in dealing with differential equations whatever it might be. But basically all these ideas of decomposition into sinusoidal components of thinking of a wild class of signals as a combination of sine waves is attributed to Fourier. So what we have done here is now to go from a discrete frequency axis. You had discrete values of the angular frequency all multiples of a fundamental frequency including the 0. We are going from discrete values of capital omega to continuous values. Let us look at this quantity here. Here omega spans the entire real axis. So essentially we have gone to a continuous frequency axis and therefore this is like a transform. It is a transform of the impulse response and in fact we shall give it a name. Obviously we will call it the Fourier transform of the impulse response. Now you know we must spend a minute in understanding what a transform is. A transform is a way of recasting a signal in a different domain and if the transform is invertible as is the case with the Fourier transform you can come back to the original domain. So the signal has all this while been described in terms of its values as a function of the independent variable time perhaps or whatever the independent variable was. Now what we are doing is to think of the same signal as comprised of sinusoidal components with angular frequency ranging all over the real axis. So what we are saying effectively this is a different way of describing the same signal and it is adequate if it is invertible, adequate in the sense you have not lost something. So if you look at this transform carefully you know if we look at the expression this is like an inner product we have interpreted that before. So it is not too difficult to imagine how we can go back from the transform to the original function can we go back is the question. What I mean is can you go back from capital H omega to HT and the answer is yes. How do we do it? Well the answer is very simple use vector intuition again. So let us use vector intuition in two dimensions first. So for example suppose let us say this was the two dimensional plane in which you had a vector let us draw that vector v and these are the unit vectors here which I am going to show in green now u1 cap, u2 cap and we decompose v into its components it will show in blue this is v1 times u1 cap and this is v2 times u2 cap and v1 clearly is the inner product of v with u1 cap and v2 is the inner product of v with u2 cap. We can reconstruct v as v1 u1 cap plus v2 u2 cap this is the important idea here. How do we reconstruct a vector from its orthogonal components? Now you know here I have assumed orthogonal components so there is an issue here we do not know if these different sinusoidal components are orthogonal or not we knew it for restricting them to a period that we reasoned out at that time but we have not reasoned in general if I take the complex exponential the rotating complex number all over the time axis as I am doing here is there the same notion of orthogonality or is there not? It is an important question that we need to answer but we will do that later. At the moment let us take a finite dimensional space as we have here and we will look at what we exactly are doing to reconstruct the components essentially reconstruct the vector from its components this is the component and this is the unit way and you are taking component times the unit vector and adding it over all the components. So what we are doing is we are taking a sum summation over all dimension so to speak component in that dimension multiplied by a unit vector in that dimension. Now the question is can I use the same principle to reconstruct a signal from its Fourier transform and the answer of course is yes I said we should use vector intuition and this is the intuition that we are going to use the only thing is now we cannot do a summation we will do an integration because it is a continuum of omegas and in the next session we shall complete our discussion on how we can do this reconstruction and understand this Fourier transform a little better thank


Going on everyone Sam here with late and sports cards rip in at four boxes for Jonathan L We've got one 23 tops chrome update series hobby 123 Chronicles 123 leaf ultimate hockey and 123 Bowman you breakers delight. So good luck here Jonathan. We'll start with update hobby Yeah, good luck here Jonathan.   Yeah Nolan Jones refractor rookie a good ray or like a random ray He was good for Justin Steele a couple years there and then he became Corbin Carroll Need John Curtis back on the race I Garcia That guy was a dog Rich Hill to at 399 on the pink another ray legend there rip, baby Baddius Ward refractor That's us Taj Bradley Corbin Carroll insert rookie Riley green action stars and base Taj Bradley base rookie auto let's go on card nice one there Jonathan that'll work jingled a grom Kershaw Grayson Rodriguez for the O's Logan Allen refractor rookie and base. All right chronicles time now Jonathan red Joe Torrey to 100 Hello Alvin. Good morning is right Jackson holiday on the jersey nice one there or else or now Got Crawford David Wells Trace Gonzalez and Jordan. Laulah. Laulah That is Dustin Harris nice one there obsidian auto for the Rangers. He's a stud Yes, Andrew Roma Yes, they are unfortunately tonight Alvin. I apologize man. I apologize. Yeah, this is the last one that we're gonna head out Rockio Carlton and Babe Ruth to 1.99 Jimmy Crooks. Oh Matt Williams nice one there on the majestic America's pastime two of seven Grats on that one Jonathan Jonathan with the Giants Yeah, two a.m. Here. Yes. It is. Well 158 to be fair What time is it there? Cecil fielder like seven eight we're getting ready to stream on chipmunk slots That is Drew Jones America's pastime boys of summer autograph gold Nice one there congrats on that one Jonathan Damn Alvin's in the future 7 a.m. In the UK L8 to 1.99 nice one there And Debbie's in the Los Santos. It's there only There only five hours ahead. Yeah, I thought they were more than that Pedro I think like Asia is Pedro Martinez I thought London was like 13 hours to 49 Matt Williams. I might be how long it is to Get there. Oh Nice one there Matt Williams and Joe Cronin to 25. Oh I've we've stayed there's been I've been here past four before Yeah, I've been here past four before Breakers the light next I've been here showboe jingles. I've been here till like 232 45. Yeah There's been a few times. There's been I Could count multiple multiple times I've been here past three and there's like once or twice have been here past four Kate Clubnick Nice one there. Yeah, I'm gonna save hockey for last Taj Brooks first Miles Davis first Jace McClellan first Joe Alts first Johnny O Gates first that is a surge of Tray Sean Ward first for Kansas State We've got yellow Keon Keely to 75 true yellow for Alabama JV on Cohen to 150 purple our pink mini diamonds for Miami blue Chris Hilton junior to 150 for LSU Jury on Dickey first base auto for Oregon And first base auto Devon Neil for Kansas This one there as well Jonathan You really nice All right, we've got leaf ultimate hockey now as well Stayed up till 5 a.m. Once right, so nice. Hell. Yeah, I got my lawn Pretty much. Yeah, I'm gonna watch after this. I was gonna say I don't know I Don't know dog. That's a good question. Honestly. Oh, this is a nice little six-way Hell, yeah, man. That is gonna be we've got Pavel Bure Yadamir Yager, Matt Sundeen Timus Alane Alexander Moghili and Sergei Federov three of five nice one there game used all the way around Nice one there on the six-way game used looks like all jerseys Stayed up 24 hours playing Final Fantasy. Good Lord Ramirez Two of five is gonna be a man in round a room a two of five game use Jersey auto nice one there Man in a room a oh, that's sick, dude 22 of 25 inscribed Pete Mahovlik Mahovlich nice one there Inscribed four-time cup champ very nice one congrats on that 22 of 25 nice one Jonathan Mahovlich nice one there Mahovlich very nice pretty solid box over there for sure pretty solid box there for sure That'll do for your break there Jonathan. Thanks again for the sport buddy. Get him right out to my man


Hello and welcome to the session. In this session we are going to discuss the following question which says that prove that cos inverse of 5 by 13 minus sin inverse of 4 by 5 is equal to 5 minus sin inverse of 16 by 65. We know that sin inverse of x minus sin inverse of y is equal to pi minus sin inverse of x into square root of 1 minus y square minus y into square root of 1 minus x square. If both x and y are greater than equal to 0 and x square plus y square is greater than 1, with this key idea we shall proceed with the solution. We need to prove that cos inverse of 5 by 13 minus sin inverse of 4 by 5 is equal to 5 minus sin inverse of 16 by 65. Taking the left hand side of the expression we have cos inverse of 5 by 13 minus sin inverse of 4 by 5 first let us take cos inverse of 5 by 13 d theta which implies that 5 by 13 is equal to cos theta. All we can write cos theta is equal to 5 by 13 in a triangle ABC if theta is the angle between the lines AC and CB. We know that cos of theta is given by base upon hypotenuse that is BC upon AC which is equal to 5 by 13 so we have the value of the base BC as 5 and the value of the hypotenuse AC as 13 then we can find the value of the prependicular AB by using Pythagoras theorem. By Pythagoras theorem we have prependicular AB is equal to square root of hypotenuse square that is AC square minus base square that is BC square which is equal to square root of 13 square minus 5 square which is further equal to square root of 169 minus 25 which is given by square root of 144 equal to 12. Therefore we have value of the prependicular AB as 12. Now we know that sin of angle theta is given by prependicular upon hypotenuse that is AB upon AC which is equal to 12 by 13 which implies that theta is equal to sin inverse of 12 by 13 Now we have cos inverse of 5 by 13 is equal to theta and theta is equal to sin inverse of 12 by 13 which implies that cos inverse of 5 by 13 is equal to sin inverse of 12 by 13 Now replace cos inverse of 5 by 13 with sin inverse of 12 by 13 in the left hand side of the given expression therefore the left hand side becomes sin inverse of 12 by 13 minus sin inverse of 4 by 5 Answer and the key idea we know that sin inverse of x minus sin inverse of y is equal to pi minus sin inverse of x into square root of 1 minus y square minus y into square root of 1 minus x square provided both x and y are greater than 0 and x square plus y square is greater than 1 Here we assume x is 12 by 13 and y is 4 by 5 and we know that 12 by 13 is greater than 0 also 4 by 5 is greater than 0 and square root of 12 by 13 plus square root of 4 by 5 is greater than 1 Therefore sin inverse of 12 by 13 minus sin inverse of 4 by 5 can be written as pi minus sin inverse of 12 by 13 into square root of 1 minus 4 by 5 square minus 4 by 5 into square root of 1 minus y square minus square root of 4 by 5 sin inverse of 1 minus 12 by 13 square that is pi minus sin inverse of 12 by 13 into square root of 1 minus 16 by 25 minus 4 by 5 into square root of 1 minus 144 upon 169 This can be written as pi minus sin inverse of 12 by 13 into square root of 25 minus 16 by 25 minus 4 by 5 square root of 169 minus 144 by 169 Thus we get pi minus sin inverse of 12 by 13 into square root of 9 by 25 minus 4 by 5 into square root of 25 upon 169 Which is equal to pi minus sin inverse of 12 by 13 into 3 by 5 minus 4 by 5 into 5 upon 13 which further gives pi minus sin inverse of 36 upon 65 minus 20 upon 65 Which is equal to pi minus sin inverse of 16 upon 65 so we get sin inverse of 12 by 13 minus sin inverse of 4 by 5 as pi minus sin inverse of 16 by 65 which is equal to the right hand side Or we can also write it as sin inverse of 5 by 13 minus sin inverse of 4 by 5 is equal to pi minus sin inverse of 16 by 65 Thus we have proved our result that this sin inverse of 5 by 13 minus sin inverse of 4 by 5 is equal to pi minus sin inverse of 16 by 65 This completes our session hope you enjoyed this session


The Red Lake Police Department is asking the public to stay off the ice after two fishermen had to be rescued on Upper Red Lake over the weekend. Officers received the call Saturday afternoon about reports of two fishermen failing to return home after a fishing trip on Upper Red. A search and rescue team was sent to find the fishermen. The team discovered they were stranded on the ice that had separated from the shoreline. The fishermen were rescued on Sunday morning just after midnight and were treated for hypothermia. Due to unsafe ice conditions, fishing on both Lower Red Lake and Upper Red Lake is prohibited until the lakes are deemed safe by the Red Lake Conservation Enforcement Department. While many area lakes are experiencing similar situations with anxious anglers ready to fish, and while some smaller lakes are completely froze over, others are not creating a dangerous situation. From the recent events in Red Lake where the ice separated and drifted away, authorities say those anglers are lucky to be alive. Ice sheet can float out very far depending on which way the wind is blowing, and they can be in pretty tough circumstances in a hurry in a situation like that. If you do venture out onto the ice, it's highly recommended to use extreme caution and you know the lake that you're on. Local law enforcement also says to be prepared to save yourself in case you fall through the ice. This time of year, we recommend that if people are venturing out onto ice, they have ice picks handy and they're ready to save themselves because a rescue crew may not be nearby to save them. To find out the latest ice conditions, Sheriff Hodepp says to call your local bait shops to get the latest ice depth information. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


I mean, just being comfortable out there, just getting a feel for the game. Preseason helped a lot. I feel like getting those reps and training camp and stuff like that all played a part. Like I said, being comfortable out there and just playing my game, just believing in myself. Do you like taking on the other team's best receiver? A good bit of time? Yeah, yeah, it's fun. I really just take whoever comes to my side, having the coaches want to play it. But yeah, it's definitely fun to compete against those guys and really just try to make them name for myself. That's kind of what I want to do. How did you come up with that? It's definitely grown a good bit since the start of the season.  Like I said, once you're comfortable out there, you can do new things. You're able to give a changeup, how to receive it's guessing. So I feel like that's my main thing. I kind of having them guessing, not knowing, obviously not knowing what coverage is but how I'm going to play them type. How much were you aware of? I mean, I'm good. Just had to play through it Sunday and I'll be ready to go come Sunday. Free will mention after they get a strip sack, you just kind of have them let it happen. What are the challenges there?   You may get a chance to get something on bad balls, but it's kind of tough playing man. You got to just let them come to you when we are and zone coverage is you got your eyes on a quarterback, you got chances sometimes. But I feel like a lot of quarterbacks are being smart with the ball now. Our pass rush are getting to them, so they're kind of taking the sack, they're getting their sack. So it's kind of tough when the front, it's not tough, we love it. We want the guys to get their sack. So that's kind of the main thing that I'll say that plays a part.  Definitely, I do that with everybody, just trying to play the game with them. I don't want to give them anything easy. Just want to be able to trick him into doing some young rookie quarterback mistakes, and that's kind of what we want to get after this week. Corey is a really good receiver, happy for him at his new home. He's a really good receiver. He's a physical receiver, a good rower-under. And he can play at all three levels of the field, so we got to make sure that we cover him at all levels. It was fun going against him last year. I got to get some one-on-one reps, so I watched him, re-watched him, watched practice from last year, and just pick up on the new things that he's added to his game, that's so far this year. It seems like Farley in the last year, you had any conversations with him about how you kind of endured what you did and emerged where you are now, Yeah, just trying to tell him to stay on it off the field. You got to stay in your playbook. So when you are ready, you'll be able to come in, step right in, the coaches will have faith in you to come in. That's the main message to him. It can be challenging mentally as a rookie. You come in and you expect to make an impact, but once you get hurt, it's kind of like, dang, where do I go from here? So I just want to make sure that he stays on his playbook and that he has to be ready when his time comes.