Question

use a reference angle to find the exact value of the following expression. do not use a calculator. cos (150°)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. cos (150°)=
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. rationalize all denominators.)
b. the answer is undefined.

Explanation:

Step1: Determine the reference angle

The angle $150^{\circ}$ is in the second - quadrant. The reference angle $\theta_{r}$ for an angle $\theta = 150^{\circ}$ is $180^{\circ}-150^{\circ}=30^{\circ}$.

Step2: Use the sign of cosine in the second - quadrant

In the second - quadrant, the cosine function is negative. We know that $\cos(30^{\circ})=\frac{\sqrt{3}}{2}$. So, $\cos(150^{\circ})=-\cos(30^{\circ})$.

Answer:

A. $\cos(150^{\circ})=-\frac{\sqrt{3}}{2}$