Question

use reference angles to find the exact value of the following expression.
(\tan\frac{7pi}{3})
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(\bigcirc) a. (\tan\frac{7pi}{3}=square)
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize the denominator.)
(\bigcirc) b. the answer is undefined.

Explanation:

Step1: Find coterminal angle

Subtract $2\pi$ from $\frac{7\pi}{3}$: $\frac{7\pi}{3}-2\pi=\frac{7\pi}{3}-\frac{6\pi}{3}=\frac{\pi}{3}$.

Step2: Find reference angle

Since $\frac{\pi}{3}$ is in the first quadrant, its reference angle is itself, $\frac{\pi}{3}$.

Step3: Evaluate tangent

We know that $\tan\frac{\pi}{3}=\sqrt{3}$, and tangent has a period of $\pi$, so $\tan\frac{7\pi}{3}=\tan\frac{\pi}{3}=\sqrt{3}$.

Answer:

A. $\tan \frac{7\pi}{3} = \sqrt{3}$