Question

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

Explanation:

Step1: Use the property of sine function $\sin(-\alpha)=-\sin\alpha$

$$\sin\frac{-5\pi}{6}=-\sin\frac{5\pi}{6}$$

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

We know that $\frac{5\pi}{6}$ is in the second quadrant, and $\sin\frac{\pi}{6}=\frac{1}{2}$, $\sin\frac{5\pi}{6}=\sin(\pi - \frac{\pi}{6})=\sin\frac{\pi}{6}=\frac{1}{2}$

Step3: Calculate the final value

Substitute $\sin\frac{5\pi}{6}=\frac{1}{2}$ into $-\sin\frac{5\pi}{6}$
$$-\sin\frac{5\pi}{6}=-\frac{1}{2}$$

Answer:

$-\frac{1}{2}$