Question

find the exact value of the following expression. do not use a calculator to enter a decimal approximation.

\\( \sin \frac { 7 \pi } { 6 } \\)

\\( \sin \frac { 7 \pi } { 6 } = \square \\)
(type an integer or a fraction. type an exact answer using radicals as needed. rationalize all denominators.)

Explanation:

Step1: Convert angle to reference angle

$\frac{7\pi}{6}=\pi+\frac{\pi}{6}$.
Since $\sin(\pi + \alpha)=-\sin\alpha$, here $\alpha = \frac{\pi}{6}$.

Step2: Find the value of $\sin\frac{\pi}{6}$

We know that $\sin\frac{\pi}{6}=\frac{1}{2}$.
So, $\sin\frac{7\pi}{6}=-\sin\frac{\pi}{6}$.

Answer:

$-\frac{1}{2}$