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Question 21 ptsThe Chebyshev polynomial of order 6 is Ts (c) = :3226 49.4 1912 =13226 49r4 + 19x2 _ 13226 49.4 1822 _ 13216 4814 18x2 ~13216 49x4 + 19x2 ~1...

Question

Question 21 ptsThe Chebyshev polynomial of order 6 is Ts (c) = :3226 49.4 1912 =13226 49r4 + 19x2 _ 13226 49.4 1822 _ 13216 4814 18x2 ~13216 49x4 + 19x2 ~1

Question 2 1 pts The Chebyshev polynomial of order 6 is Ts (c) = : 3226 49.4 1912 =1 3226 49r4 + 19x2 _ 1 3226 49.4 1822 _ 1 3216 4814 18x2 ~1 3216 49x4 + 19x2 ~1



Answers

Use de Moivre's Theorem to find each of the following. Write your answer in standard form. $$\left(\sqrt{2} \operatorname{cis} \frac{7 \pi}{18}\right)^{6}$$

We'll use the moderates there, um, to raise this complex number to the fourth power. So the term says, Take the Ma Jealous, which is three. Raise it to the fourth power. Take the angle multiplied by four. So 45 or six there, plus I sine for five or six three to the fourth. That's 39 2081 for pyro six. That's the same is two pi or three. That's 60 degrees in the second quadrant. It's where 23 negative 12 So the cosine is negative one half, and the sign is the square to three over to to get negative 81 house plus 81 I square to three over to.

In this problem let us look at the equation which is given to us, This is two times sign off to explain minus five by six minus three cars off two weeks. Yes, five by three was equals two. Thanks. The only way that this can be done is that This should be equal to -1 and this should be equal to what? Yeah, because the maximum value of minus three costs to express five by 33. That's when cost values -1 and the maximally have to sign them is to and that's when signed them is equal to one. And that's only You can get the right and service five. This means that two expired 3 -3 five and 6 should be equal stupid. All right. Which means that two X by three equals 25 by two plus biometrics. Which is To buy my three. Or we get x. s. equals two. Right from here. We get that two X plus By my three should be equals two. Bye. Or two weeks equals two, 253 or X. S equals two. Bye bye. And we see that from both sides we get different access. So there is no solution X belongs to. Sorry. Not so

Okay, We're gonna raise this one, plus I to the Six Powers. So one of our choice is to actually multiplied out six times. That's no good. Let's just go ahead and change it to its, uh, triggered a metric forum. It's one on the X one on the Y Square to is the partners. So this is squared it to CS and then is 45 degrees okay, that's too hard to multiply by six. I'm gonna change it to Piper for So it's the square to to to the sixth CS six pi over four, 248 So that's eight CS three pi over two, 35 or two. That would be here. And it's name is zero on the X negative one on the y. So this eight times zero plus negative one I, which is negative eight. I

This problem asks us to evaluate the inverse CO sign off the negative of Negative Square to three over two. And so it's asking us what angle has a co sign of the negative square to three over two. Well, we've been working with the unit circle and in the unit circle. We know that we are looking for a co signed value when it's negative and conduct, too. So we can pretty much pass all this stuff You're in quadrant one and head on over to quadrant to looking for an ex value. Because, remember, I is associated with the X value off the order Pear sign is associate ID with the Y values. So we need an X value. It has a negative square to three over two, and here it is, and the angle associated with that 150 degrees or five pie over six radiance again in Trig. What I mostly dealing with radiance per burn unit of measure. So five pi over six radiance


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