Find each exact function value. See Example 3.
sin (-8π/...

Question

Find each exact function value. See Example 3.

sin (-8π/ 3)

Accepted Answer

Hello, everyone. We are asked to determine the exact value of the given function. We are given the sign of negative 10 pi divided by three. Our answer choices are a, the square root of three B, the square root of three divided by two C negative square root of three divided by two D negative one half. First recall that sign is an odd function. So this means that the sign of negative 10 pi divided by three is equal to the negative sign of 10 pie divided by three. So this means we go counterclockwise around the circle and we need to find an acute angle that has the same S value as negative sine of 10 pi divided by three. And that would be the sine of pi divided by three. So now to find the sine of pi divided by three, we can use a special right triangle. I recall that pi divided by three has the same value as 60 degrees. And that there's a special right triangle that is a 30 60 90 right triangle. So we're gonna use that. So I'm gonna draw myself a right triangle. I'm gonna name it JKL with K being at my 90 degree angle angle L is going to be my 60 degree angle which I'm going to label as pi divided by three angle J will be my 30 degree angle which I will label as pi divided by six. I recall in a 30 60 90 triangle, the hypotenuse has a measure of two. The side across from 30 degrees has a measure of one and the side across from 60 degrees has a measure of the square root of three. So now to find the sign of pi divided by three, which is at angle L I want the side, opposite angle L which is side JK. And I'm going to divide that by the hypotenuse which is side JL JK has a measure of radical three. JL has a measure of two. So this means that the sign of pi divided by three is equal to radical three divided by two. And since we tracked that all the way back to being equal to the sine of negative 10 pi divided by three, this is our answer. It's answer choice B the square root of three divided by two have a good day.

Struggling with Trigonometry?

Find each exact function value. See Example 3.
sin (-8π/ 3)

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Complementary and Supplementary Angles practice set

Struggling with Trigonometry?

Find each exact function value. See Example 3.sin (-8π/ 3)

Watch next

Complementary and Supplementary Angles practice set

Find each exact function value. See Example 3.
sin (-8π/ 3)