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Practice QuestionsIn cach part, list the nubers askerl for. Use trigonometry to simplily your MSWCTS Hch {5 possible. preferably so the sine ad cosine finctions do ...

Question

Practice QuestionsIn cach part, list the nubers askerl for. Use trigonometry to simplily your MSWCTS Hch {5 possible. preferably so the sine ad cosine finctions do not appear in YOur anSWeTS. (For exaple; one of the twellth roots of unity is COS 22 + i sin 22 Note thac %5 & radians is 309 _ If you recall (or calculate) that the cosine ad sine of a 309 angle are v and { respeetively, then you can write this numher as Yi+i: ! J+ There are eleven other twellth roots of unity:) As general fact,

Practice Questions In cach part, list the nubers askerl for. Use trigonometry to simplily your MSWCTS Hch {5 possible. preferably so the sine ad cosine finctions do not appear in YOur anSWeTS. (For exaple; one of the twellth roots of unity is COS 22 + i sin 22 Note thac %5 & radians is 309 _ If you recall (or calculate) that the cosine ad sine of a 309 angle are v and { respeetively, then you can write this numher as Yi+i: ! J+ There are eleven other twellth roots of unity:) As general fact, il you calculate 2 cOS 2) +isin 4 then equation (3) shows that each of the other n-th roots of unity is a power o 2. Find the two second roots (also calledl square roots) of unity: 2. Find the three third roots (or cuhe roots) o unity: Find the four fourth roots of unity: 4. Find the six sixth roots of unity:



Answers

For the following exercises, find the reference angle, the quadrant of the terminal side, and the sine and cosine of each angle. If the angle is not one of the angles on the unit circle, use a calculator and round to three decimal places.
$$
\frac{5 \pi}{3}
$$

This question is asking us to find the reference angle quarter of the Trimmel side and Sun Co sign of each angle. In this context, we're looking at two pi over three, not its first imperative that we analyze what quadrant this is that we know that this is somewhere between pi over too, and pie their forts in the second quadrant somewhere over here. Therefore, we know we can take the slightly bigger angle pie and do pie subtracting two pi over three in order to obtain pi over three, which is our reference angle. Remember, the second piece of information is the quarter of the terminal side we're looking at. The diagram is quadrant to now. You're asked you the unit circle to find Sinan Cosa using the unit circle looking at two pi over three as one of the special angles on the unit circle, we end up with coordinates of negative 1/2 com a squirt of three over to not remember We name our coordinate points. Co sign. Calm aside. We know coastline is always first. Therefore, coastline is negative. 1/2 scientists positive squirt of three over two

This question addresses the given angle. Five. Pi over four. I need to find the reference angle quadrant in which it lies as well as the sign. Five. Pi over four in the post Sign five Pi over four. Let's just begin. Bye. Giving ourselves a visual of the craft. Five. Pi over four. So that's one and 1/4 of potty is part of a two. There's pie Live pie over four that looks pretty good. We can record right away that the terminal side is in Quadrant three, and we can quickly determined that the reference angle here is pi over four. That was a result of the calculation. Five. Pie over four minus pi, which is Samos five. Pie over four, but it's four pi over four that would have yielded high over four. So that's our reference angle. In finding the signing coast sign of this given angle, we're actually going to find the sign off Pi over four in Quadrant three and the Coast Sign of Pi over four in Quadrant three. We could do that in so many different ways, but really quickly sign of pile before it's radical to over two Sinus negative in the third quadrant, so he signed the native sign co sign. Also high over four would be negative to over two. Also negative. In the third quadrant, you would've signed the negative. You wanted to see exactly what this tryingto looked like here. This would have been our pi over four. We would have had the red to over two, the red to over two. And, of course, the radius of one.

First part we have given sign off angle B is equal passport photo divided by so this is equal to one divided by a squared photo booth. This is equal to sign a 45 degree, and this is also equal to sign off for 35 degrees. So angle we can be equal to 45. The very end 1 35 degree in part B. We have course sign off is equally disparate. Oh, poor divide by two. This is equal to one divide by sparrow. Talk to, and this is equal to course, off 45 degree vigor. Angle is equal to 45 dignity. In Part C. We have signed off. It is equal to one day wear by four vigor at is required to sign in worse one. The word by four. This is 1/4 14.5 degrees. Another angle will be equal to 22 degree, Minor said. This is a part of learning to degree minus 14.5 we get. This is equal to 1 65 0.5 degrees in the part we have for sign off. K is equal to minus two. Divided by three, we get K is equal to course in worse off minor story whereby TV Get Basic Oneto 1 21.8 Big Aries

Oh, you're signed This problem A and B are pretty much the same question. I'm not sure how to differentiate how toe how to explain this. Um, but if you think about on the unit circle because, um, you know, we are just rotating the entire time with a It's called the unit circle, cause the radius is one, um, everything about if you're just adding pirate to radiance or 90 degrees. Ah, What it boils down to is the ordered pair. I'll say a B along the way. It's just going to be negated and flipped. So, like, this order pairs negative B A and you can do that with any point along the unit circle. Um, so I don't say here at this point over here and you have a 90 degree turn. Um, so we have the order. Pair A B over here is going to become negative B A. And it works. Even if you were to rotate this over this way again, you just have toe flip it again. So every negative, a negative b And if you did another one, um, on the side, so flip it in the gate. So BB negative a so you can sort of see along the way. What's happening is the X coordinate becomes the y. Coordinate. Uh, the Y coordinate becomes the X coordinate and negated. And that's the rule I was doing. So, uh, the white corn, it becomes the X coordinate union gate, that one, and then the other one stays the same, but becomes a lie Cornet. So the white corn, it becomes the X coordinate and it's negated. And then that x cordant just becomes the like order and I could do it one more time. You can see the negation, and then this one stays the same, but just switches eso Well, how does that sort of explain for for part B is ah is the form that they have written is it is explaining exactly that. So since co sign is the X coordinate, you just switch it and negated eight a plus pyre or two. Uh, you switch it. I don Athena and you negated and then sign you notice So hopefully you can write down in better words than what I'm doing is you just switch it, uh, which is exactly what they're saying. So for parts seeing this problem. Um, just go to a calculator for for I And I guess one and two they switched the Roman numerals. Um, just make sure you're in radiant mode. Whatever you get for each answer, I don't know because they're not in the unit circle. Um, you'll get the same exact decimal. That's what you're trying to verify now for three and four switch over to degree mode. But just like what I mentioned before, it's the same exact decimal. That's what they're looking for.


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