Find each exact function value. See Example 3.
tan (-1...

Question

Find each exact function value. See Example 3.

tan (-14π/ 3)

Accepted Answer

Hello, everyone. We want to determine the exact value of the given function. The function we are given is the tangent of negative 11 pi divided by three. Our answer choices are a negative one half B negative radical three divided by two C radical 3d negative radical three. First recall that tangent is an odd function. So the tangent of negative 11 pi divided by three is equal to the negative tangent of 11 pi divided by three. This means if we started in standard position, we'd be going counterclockwise. And when we do so the negative tangent of 11 pi divided by three would equal the same as the tangent of pi divided by three. So we're going to work to solve the tangent of pi divided by three. We're going to use a special right triangle. And I recall that pi divided by three is equal to 60 degrees. And I recall we have a special right triangle that would be 30 60 90 degrees. So that's what I'm gonna use as my basis. So I'm drawing myself a right triangle. I'm gonna label the corners JK and L with my right angle at angle K and I'm putting pie over three instead of 60 degrees at angle L, I'm putting pi divided by six at angle J for my 30 degree angle. And I recall that the ratio here is that the side across from the 30 degree angle which is pi divided by six has a value of one. The hypotenuse has a value of two and the leg across from the 60 degree angle or pi divided by three has a value of the square root of three. So now to find the tangent of pi divided by three, I need the opposite side. So the side that's opposite angle, L which is angle or sorry side JK, I'm gonna divide that by the side that's adjacent to angle L. So side Kl and the measures there JK has a measure of radical three. Kl has a measure of one. So this means that the tangent of pi divided by three is equal to the square root of three. And that is our answer. So radical three or the square root of three which is answer choice C have a nice day.

Find each exact function value. See Example 3.
tan (-14π/ 3)

Key Concepts

Unit Circle

Periodic Functions

Reference Angles

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