Question

find the exact value.

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

type + or -

\\( \frac { ? } { } \\)

Explanation:

Step1: Use the property of sine function

We know that \(\sin(-\alpha)=-\sin\alpha\). So, \(\sin\frac{-7\pi}{6}=-\sin\frac{7\pi}{6}\).

Step2: Find the reference angle

\(\frac{7\pi}{6}=\pi+\frac{\pi}{6}\). The reference angle for \(\frac{7\pi}{6}\) is \(\frac{\pi}{6}\). And \(\sin\frac{7\pi}{6}=-\sin\frac{\pi}{6}\) (since \(\frac{7\pi}{6}\) is in the third - quadrant where sine is negative).

Step3: Calculate the value

Since \(\sin\frac{\pi}{6}=\frac{1}{2}\), then \(\sin\frac{7\pi}{6}=-\frac{1}{2}\). And \(\sin\frac{-7\pi}{6}=-\sin\frac{7\pi}{6}\). Substituting the value of \(\sin\frac{7\pi}{6}\), we get \(\sin\frac{-7\pi}{6}=\frac{1}{2}\).

Answer:

\(+\)