CONCEPT PREVIEW Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all. I II 1. A. √3 2. B. 1 3. C. ½ 4. D. √3 5. csc 60° 2 6. E. 2√3 3 F. √3 3 G. 2 H. √2 2 I. √2

Video transcript

Welcome back. Everyone. In this problem, we want to determine which of the following answer choices is the exact value of the trigonometric function of the cores count of degrees. For our answer choices A is two, B is two multiplied by the square of three, all divided by three C is the square root of two and D is zero. Now, we want to find the exact value of the and what do we know about the? Well, recall that the cores of an anger is the reciprocal of its sign. So what this tells us then is that the co sequent of 45 degrees must be equal to one divided by the sign of 45 degrees. Now, we're on our way, we just need to figure out what the sign of 45 degrees is. Let's use our unit triangle to help us. Now, on our unit right triangle, we know that when our anger theta equals 45 degrees, then the length of each side of our triangle is one. OK. We also know that if the length of both sides is one, then to find the length of the longest side, the hypo, we can use Pythagoras's theorem. And by Pythagoras's theorem, it tells us then that the length of the long side, the hypotenuse squared. So let's call that X squared, X squared would be equal to the sum of the squares of the two shorter sides, which would be one squared plus one squared, one squared is one and one plus one equals two. So that means the length of our hypos equals the square root of two because we'd find the square root of both sides to get X by itself. So our unknown side then is the square root of two. Now, do we know anything else that can help us? Well, we also know that the sign ratio, we also know that the sign ratio equals the opposite side to the hypotenuse. So that means that the sign of 45 degrees equals the opposite side, which is 12, the hypotenuse which is the square root of two, that would be the exact value of the sign of 45 degrees. So we can substitute that value into our expression into our expression here because since the sign of 45 degrees equals one divided by the square of two, then I can rewrite that as one divided by one, divided by the square of two, which if I write it out, one divided by one divided by the square of two, and I can change this to multiply so that one multiplied by the square of two divided by one which equals the square of two. Therefore, the cos of 45 degrees is the square root of two. When we look back on our answer choices, that would have been answer choice. C Thanks a lot for watching everyone. I hope this video helped.