Question

What is the sine value of 7 pi over 6?

Answer 1

Since $\sin(\pi-x)=\sin x$, you have

$\sin\dfrac{7\pi}6=\sin\left(\pi-\dfrac{7\pi}6\right)=\sin\left(-\dfrac\pi6\right)$

and since $\sin x$ is odd, i.e. $\sin(-x)=-\sin x$, you have

$\sin\dfrac{7\pi}6=-\sin\dfrac\pi6=-\dfrac12$