What did mrs margarine think about answer key

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In Exercises 1– 8, evaluate each expression (a) $\cos (2 \pi / 3)$ (b) $\cos (-2 \pi / 3)$ (c) $\sin (2 \pi / 3)$ (d) $\sin (-2 \pi / 3)$

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Video Transcript

Okay, so we want to find the falling value used for these expressions here. So it's not that we have two pi over three. So where is two pi? Over three? What? That's almost pie. So that means we're gonna be in quadrant to. So you wanted to our X value where a coast on value is negative and our sign value is positive. Now, let's also look at negative two part of three. So we're gonna go to shit amount, but in our clockwise direction, and then we're gonna end up in quadrants. Three. I'm quite injury. Our coast on value is negative, and our sign value is positive. Now we want to refer to our pi over three inclusions. One. So in quadrant one, we have, however drain. And we know that this is our longer side. So this is going to be the square root of dream. This is going to be one that our hypothesis too. So co sign of two pi over three. That's the same eyes we said in Quadrant two. We have two pi over three. Military negative to part three Here, Jarkko sign is negative. So we're gonna write that as a negative coastline of our angle part of a three. So this is equal to negative 1/2 for native to par victory. Again, we have negative co sign of pi over three semantical to negative 1/2. And what about sign of two pi over three, he said. Sinus posture. So that's going to be the same value as that of Pirate Bay. So we have sign of part of agree, and that's equal to a, um, square root of 3/2 and actually made a mistake here. Sign should not be positive, since we are below our X axis, so this should be negative. It's a sign of negative two pi over three that's going to be negative. Sign both part of a three, which is equal to negative square roots of 3/2.

Video Transcript

Okay. So it says, what did mrs margarine think about her sister's husband. So we have A total of 24 problems on here. Um So the way that you solve this is you have sine cosine tangent When you're looking at a triangle, remember sine is the opposite over the hypotenuse. Cosine is the adjacent over the hypotenuse and the tangent is the opposite over the adjacent. Okay, remember the hypotenuse is the longest side. Uh In all of these triangles, it's the opposite from the right angle. Okay so let's go through these number one, we're looking for the sign. So remember that's opposite over the hypotenuse. So that would be um five over 13. Number two would be co sign of A. So that would be the side adjacent or next to A. And then over the hypotenuse. So that would be 12/13. And then number three is tangent of A. So that would be the um opposite side. Five over the adjacent side. 12. So it would be 5/12. Uh Number four We're looking at um the same triangle but we're looking at B. So again we have sine cosine tangent. Sine is opposite over hypotenuse. So that would be 12/13. Number five would be cosine. So that's adjacent over hypotenuse, that would be 5/13. And number six would be tangent of B. Which is adjacent, I'm sorry, opposite over adjacent. And that would be 12/5. Number seven, we're looking at another new triangle here. And we have sine Cosine tangent of A. So sign of A. Would be opposite over hypotenuse. So that would be 1/2 eight would be co sign A. So that would be adjacent over hypotenuse which would be the square root of 3/2 and nine would be tangent of A. So that would be um opposite over adjacent. So one over the square root of three. Now we're looking at the same triangle and we're doing um angle B. So sign of B would be opposite over hypotenuse. So that would be the square root of 3/2. Number 11 would be the coastline so adjacent over hypotenuse. So that's one half and number 12 would be the tangent of B which would be opposite over adjacent. So it would be um The square root of three over one, Which is just the square root of three. Number 13. We're looking at a new triangle. We have sine cosine and tangent. So again sign uh is opposite over hypotenuse. So we would end up with 12 15th which would be 4/5 Number 14 would be a coastline. So that would be adjacent over hypotenuse which would be 9/15, which would be 3/5 Number 15 would be tangent Which is opposite over adjacent. So that would be 12/9 which is 4/3 number 16. Same triangle. But now we're dealing with angle B. We have sine cosine and tangent A member sine is opposite over hypotenuse. So that would be seven over the square root of 58. Number 17 would be adjacent over hypotenuse for the coastline. And that would be three Over the square root of 58. And then 18 would be the tangent which is opposite over adjacent, which is 7/3. Let's see. We have 19 which we're dealing with a new triangle now. So we have sine cosine tangent of angle. A sign a would be opposite over hypotenuse which would be 16 Over 34, which is eight over 17. Number 20 would be co sign adjacent over hypotenuse. So that would be 30/34 which equals 15. That'll be 15/17. Number 21 would be tangent. So that would be opposite over adjacent or 16/30 which would be 8/15. Then we have 22 dealing with the same triangle. But we're doing actually, it's a new triangle sign. Um of a coastline of a tangent of a so sign would be opposite over hypotenuse. So that would be one over the square root of two. Number 23 is the co sign of a. So that would be the adjacent over hypotenuse which would be one over square root of two and 24 is the tangent. So that would be opposite over adjacent, which would be 1/1, which would equal one. Um And then if you take all of these and you plug it into the answers you're gonna get. He is a terrific butter in law. Okay