Question

10 multiple choice 1 point
find the exact value of ( sin left(-\frac{5 pi}{6} \text { radians }
ight) ).
( -\frac{1}{2} )
-1
( -\frac{sqrt{3}}{2} )
( -\frac{sqrt{2}}{2} )

Explanation:

Step1: Use the property of sine function

The property of sine function: $\sin(-\alpha)=-\sin\alpha$. So, $\sin(-\frac{5\pi}{6}) = -\sin(\frac{5\pi}{6})$.

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

We know that $\frac{5\pi}{6}=\pi-\frac{\pi}{6}$. And $\sin(\pi - \theta)=\sin\theta$. So, $\sin(\frac{5\pi}{6})=\sin(\pi-\frac{\pi}{6})=\sin(\frac{\pi}{6})$.
Since $\sin(\frac{\pi}{6})=\frac{1}{2}$.

Step3: Calculate the value of $\sin(-\frac{5\pi}{6})$

Substitute the value of $\sin(\frac{5\pi}{6})$ into the expression in Step1. We get $\sin(-\frac{5\pi}{6})=-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$ (corresponding to the first option)