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FinJ the Aca bovnlel 63 Je Cutve 2 = @ Cos @ 9&= aSin & 0 <0 Szt @nd the lines 4 =0 4 x =0...

Question

FinJ the Aca bovnlel 63 Je Cutve 2 = @ Cos @ 9&= aSin & 0 <0 Szt @nd the lines 4 =0 4 x =0

FinJ the Aca bovnlel 63 Je Cutve 2 = @ Cos @ 9&= aSin & 0 <0 Szt @nd the lines 4 =0 4 x =0



Answers

In Exercises 59-62, use the Quadratic Formula to solve the equation in the interval $ [0, 2\pi) $. Then use a graphing utility to approximate the angle $ x $.

$ 4 \cos^2 x - 4 \cos x - 1 = 0 $

Okay, So first I'm going to figure out when is co signed equal to zero. So on the unit circle Kassian represents X and X is equal to zero on the Y axis, which happens exactly twice. So this happens at Pirate Two in three pi over two? I think so. My final answers are higher or two, and then the period of cosign plus two pi times n and then three pi over two in the period, This plus two pi and And I could actually change this to just one equation, right? Because if I add hi, which is the same thing is to pipe or two. Then I can combine this into my final solution, which will be pi over two plus pi times and which will account for 35 or two equations. Now, I'm not completely finish it because my angle is X over four. So x over four equals this solution, and I still want to get X by itself. So I'm gonna multiplied by four to both sides, and when I'm multiplied to the right side, I'm going to distribute for to each side. So my final solution will be, um, four times to a cancel. So this will be to plot pi plus four hi times. End will be my final solution.

The gun equation is four times off. Assign Skirt six minus four co sign IX. Unless one is well, it's 20 on. We have to solve the equation without using the calculator. So let's proceed with the solution that is a zoom. Why is equal to Kasai Nix? So the question becomes four times off by square minus four. White blast one as equal to zero a student. We ask a question here why we're resuming CoSine X as a way just to simplify the equation on dhe. Get the result quickly We are is doing in this matter. So now we observed that the left side of the equation is a perfect square, which is to why minus one whole square is equal to zero. Now we can write this equation as two minus one in quotes to zero. So the value of y from here will be one divided by two and resumed Y s CO sign X. So we could say that cause Sign X is equal to one by two. From here, the value off extra will be calls to plus minus by a bay three. So finally we can write the general solution for this equation as exit called Street two. And by plus minus bye bye tree where the value off and starts from zero So plus minus +12 plus minus two on it goes on. So a student we ask a question, Harold, so that how we are able to write a general solution in this manner we know that the period function for Kasai nexus to pie. But after every two by angle the value of co sign repeats If you see the graph off course Cynics, it looks like this. This is by about two. This is zero on here it is by hair. It is three pie by two on here it is to buy. So after every two by cycle the value for Kasai next repeats. That is where able to write the general solution in this way. So I hope you got the problem. Thank you

I figured since I'm gonna need Thio, use the inverse coat sign method to solve this. It makes sense to just show you what I would do on a graphing calculator as well. So I'm showing you this one now. Technically, what I'm doing is I'm finding values for Exeter bigger than zero, but smaller than two. Pi to pie is about a little bit bigger than six. So the two answers I want our 1.7794 point 504 But the directions ask you to use a quadratic formula because this is a quadratic. The only thing is instead of X, equals its coastline of X equals andan. The formula is negative, B plus or minus. So I'm just gonna do the plus right now under the minus in the second square root of B squared, whether it's four or negative four squared, how you get a positive minus four times a times C. She is negative. One all over, two times a um So this is one answer for co sign of X. So how we solve that? As we do in verse co sign So on some calculations hit second co sign find the function somewhere in there, Uh, of that answer. So I'm just gonna copy it. Copy. I need parentheses on this calculator. Um, negative B plus or minus the square root of B squared. Oh, that makes sense, because cosine can only be a value between negative one and one. So this makes sense that that answer didn't work? Uh, it's impossible for co signed equal a number larger than one. So let's do this again. Except the quadratic to a negative. So now this is possible because this number is bigger than negative one. That this copy that equation. I started that numerical value and plug it in and get that 1.779 Now, as far as radiance goes, 1.779 is in the second quadrant. Eso if I want where quite the answer. In the third quadrant, what I can do is take too high and subtract off that numerical value. Because, remember, cosine is negative. Co sign is negative in the 2nd and 3rd quad narrate. You know, I wrote it like this. So we get the answer 4.504 So that's Ah, the algebra behind. Why are two answers are these two? 1.779 and 4.504

In this trouble given equation can be really hurting us. Eight same expo six. Last three into 1 -2. Same square of X plus two times To cost Square two weeks minus one. Last one equals to zero skin redness to send square of X. Holy cube last three, one minus two. Same square of X less. This can witness for one minus to send square of eggs whole square This is cost two weeks can be written as one man is to send square X. Since its cost square two weeks. So square time comes -2-plus 1 equals to zero. Now let us make the substitution. That why is to sign square of X. Which makes the situation as y cube Just three into one minus Y plus four and two one minus y Whole squared -1 equals to zero. Mm This is why Q plus three minus three. Y less four one plus y squared minus two. Y -1 equals to zero scan written us like you This four way square -11. Y last six equals to zero Or y plus six into Why? Square minus do I Last one equals to 0? Or y plus six. In the Y -1 Elsewhere equals to zero case one that y is minus six. This is not possible because the maximum value of two cents square access to 2nd. Why is one which means that sign X His plus -1 or what due to. Which means that access anti my two plus by all. This is the solution. Not so


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