Find each exact function value. See Example 3.
sec π/6

Question

Find each exact function value. See Example 3.

sec π/6

Accepted Answer

Welcome back, everyone in this problem, we want to determine the exact value of the function of the second of 1/4 of pi radiant. For our answer choices A is one, B is the square root of two divided by two C is the square root of two and D is two. Now, if we're going to find the exact value of our function of the second of 1/4 of pi, it would be good to think about it in a right triangle. Now, we're talking about 1/4 of py radiance, which is the same thing as 45 degrees. Do we know anything about triangles with 45 degrees? Well, recall that that's actually the unit triangle. OK. So if I were to draw that here in that right triangle where both angles are the same. 1/4 of Pians, then the length of the two smaller sides is one unit and the length of the hypotenuse is the square root of two. Now that we know the size for that triangle we should be able to solve for the CC, what do we know about the CC? We recall? OK. That the second is actually the reciprocal function of the cosine function. OK. What do we know about the cosine function? Well, we also know that the cosine of an angle equals the adjacent side or is the ratio of the adjacent side to the hypotenuse. So since the second is the reciprocal of that, that means the second of an angle in terms of the size of a right triangle would be equal to the hypotenuse or the ratio of the hypotenuse to the adjacent. Now, we know the length of the hyperten and the side that's adjacent to 1/4 of Pyridium. So we should be able to solve for the second because no, that tells us then OK, that tells us that the second of 1/4 of pie is going to be equal to the hypotenuse, which is the square root of two divided by the adjacent side. Now, because both angles are 1/4 of pi we could use either one to talk about the opposite and adjacent sides. So let's say I were to use this angle don at the bottom. Well, no, that means our adjacent side is one unit here at the base of the triangle. Our opposite side is one unit which is the height of the triangle. And as stated before, we know that our hypotenuse is the square root of two. Therefore the adjacent side is one unit. So that's the ratio of the square of 2 to 1, which tells us then that the second of 1/4 of pi is equal to the square root of two. When we look back in our answer choices, that would have been answer choice. C thanks a lot for watching everyone. I hope this video helped.

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