Question

find the exact value. sin\frac{-5\pi}{6} type + or -

Explanation:

Step1: Use the property of sine function

We know that \(\sin(-\alpha)=-\sin\alpha\). So, \(\sin\frac{-5\pi}{6}=-\sin\frac{5\pi}{6}\).

Step2: Find the value of \(\sin\frac{5\pi}{6}\)

\(\frac{5\pi}{6}\) is in the second quadrant where sine is positive. And \(\sin\frac{5\pi}{6}=\sin(\pi - \frac{\pi}{6})\). Using the formula \(\sin(\pi-\alpha)=\sin\alpha\), we get \(\sin(\pi - \frac{\pi}{6})=\sin\frac{\pi}{6}\). Since \(\sin\frac{\pi}{6}=\frac{1}{2}\).

Step3: Calculate the final value

Substitute \(\sin\frac{5\pi}{6}=\frac{1}{2}\) into \(-\sin\frac{5\pi}{6}\), we get \(-\frac{1}{2}\).

Answer:

\(-\frac{1}{2}\)