use the reference angle to find the exact value of the given expression. sin(-11π/6) select the correct…

use the reference angle to find the exact value of the given expression. sin(-11π/6) select the correct choice below and fill in any answer boxes in your choice. a. sin(-11π/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(-11π/6) select the correct choice below and fill in any answer boxes in your choice. a. sin(-11π/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: Find the positive - equivalent angle

Add (2\pi) to (-\frac{11\pi}{6}). Since (2\pi=\frac{12\pi}{6}), then (-\frac{11\pi}{6}+ \frac{12\pi}{6}=\frac{\pi}{6}).

Step2: Determine the sign of the sine value

The angle (-\frac{11\pi}{6}) is in the first - quadrant. The sine function is positive in the first - quadrant. And we know that (\sin\theta) has the same value as (\sin) of its reference angle in the first - quadrant. Also, (\sin\left(\frac{\pi}{6}\right)=\frac{1}{2}). So (\sin\left(-\frac{11\pi}{6}\right)=\frac{1}{2}).

Answer:

A. (\sin\left(-\frac{11\pi}{6}\right)=\frac{1}{2})