Find each exact function value. See Example 3.
tan 5π/3

Question

Find each exact function value. See Example 3.

tan 5π/3

Accepted Answer

Hello, everyone. We are asked to determine the exact value of the given function. We are given the tangent of two pi divided by three. Our answer choices are a one B radical three divided by two C radical three divided by 3d negative radical three. First, I notice that two pi divided by three is an obtuse angle. I want to find a reference angle that will match this. So the tangent of two pi divided by three is equal to the negative tangent of pi divided by three. So now that I'm working with an acute angle, I can go forward and use a special right triangle. So pi divided by three is equal to 60 degrees. And I recall that we had a 30 60 90 special right triangle. So this means 30 is the same as pi divided by 660 is the same as pi divided by three and 90 is pi divided by two. So I'm going to draw that special right triangle. I'm gonna label it JKL. My right angle is at angle K. I'm gonna put the 30 or Pi divided by six at angle J and the 60 or Pi divided by three at angle L. So we're calling a 30 60 90 triangle. The hypotenuse has a measure of two, the side across from the 30 degree angle or in this case, pi divided by six angle has a measure of one and the side across from the pi divided by three angle has a measure of the square root of three. So now I'm gonna start out by looking for the tangent of pi divided by three pi divided by three is at angle L and I recall that tangent is the opposite side divided by the adjacent side. So the opposite side is side JK, the adjacent side is side. Kl, 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 the square root of three. However, if you recall, we were looking for the negative tangent. So this means I'm gonna multiply both sides by negative one. So the negative tangent of pi divided by three, what do you call the negative square root of three? So I can say that the tangent of two pi divided by three is equal to negative radical three. That is our answer and it matches answer choice D have a nice day.

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Find each exact function value. See Example 3.
tan 5π/3

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Find each exact function value. See Example 3.tan 5π/3

Watch next

Complementary and Supplementary Angles practice set

Find each exact function value. See Example 3.
tan 5π/3