Question

use reference angles to find the exact value of the following expression. cos(7π/6)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. cos(7π/6)=
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize the denominator.)
b. the answer is undefined.

Explanation:

Step1: Find the reference angle

The angle $\frac{7\pi}{6}$ is in the third - quadrant. To find the reference angle $\theta'$, we use the formula $\theta'=\frac{7\pi}{6}-\pi=\frac{7\pi - 6\pi}{6}=\frac{\pi}{6}$.

Step2: Determine the sign of cosine in the third - quadrant

In the third - quadrant, the cosine function is negative.

Step3: Find the value of cosine of the reference angle

We know that $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}$. Since $\cos\frac{7\pi}{6}$ is negative in the third - quadrant, $\cos\frac{7\pi}{6}=-\cos\frac{\pi}{6}$.
So, $\cos\frac{7\pi}{6}=-\frac{\sqrt{3}}{2}$.

Answer:

A. $\cos\frac{7\pi}{6}=-\frac{\sqrt{3}}{2}$