Question

use reference angles to find the exact value of the following expression. do not use a calculator. sin(-150°)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. sin(-150°)=
(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 positive - equivalent angle

Since the sine function is odd, $\sin(-\theta)=-\sin\theta$. So, $\sin(- 150^{\circ})=-\sin(150^{\circ})$.

Step2: Determine the reference angle

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

Step3: Evaluate the sine of the reference angle

We know that $\sin(30^{\circ})=\frac{1}{2}$. And for an angle in the second - quadrant, $\sin\theta>0$. So, $\sin(150^{\circ})=\sin(30^{\circ})=\frac{1}{2}$.

Step4: Find the value of $\sin(-150^{\circ})$

Since $\sin(-150^{\circ})=-\sin(150^{\circ})$, then $\sin(-150^{\circ})=-\frac{1}{2}$.

Answer:

A. $\sin(-150^{\circ})=-\frac{1}{2}$