use the reference angle to find the exact value of the given expression. sin 5π/6 select the correct choice…

use the reference angle to find the exact value of the given expression. sin 5π/6 select the correct choice below and fill in any answer boxes in your choice. a. sin 5π/6 = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. type an exact answer, using radicals as needed.) b. the answer is undefined.

use the reference angle to find the exact value of the given expression. sin 5π/6 select the correct choice below and fill in any answer boxes in your choice. a. sin 5π/6 = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. type an exact answer, using radicals as needed.) b. the answer is undefined.

Answer

Explanation:

Step1: Determine the reference angle

The angle $\frac{5\pi}{6}$ is in the second - quadrant. The reference angle $\theta'$ for an angle $\theta=\frac{5\pi}{6}$ is $\pi-\frac{5\pi}{6}=\frac{\pi}{6}$.

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

In the second - quadrant, sine is positive. And we know that $\sin\theta=\sin\theta'$ for $\theta$ in the second - quadrant. Since $\sin\frac{\pi}{6}=\frac{1}{2}$, then $\sin\frac{5\pi}{6}=\frac{1}{2}$.

Answer:

A. $\sin\frac{5\pi}{6}=\frac{1}{2}$