Question

Value of $\sin (-{420}^{\circ })$ is

• A. $\frac{1}{2}$
• B. $-\frac{\sqrt{3}}{2}$
• C. $\frac{-1}{2}$

Answer 1

The correct option is B $-\frac{\sqrt{3}}{2}$

$\sin (-420°)=-\sin (420°)=-\sin (360°+60°)=-\sin (60°)=-\frac{\sqrt{3}}{2}$
or
$\sin (-420°)=\sin (-(450°-30°\left)\right)=\sin (-450°+30°)=\sin (-\frac{5\pi }{2}+\frac{\pi }{6})=-\cos \left(\frac{\pi }{6}\right)=-\frac{\sqrt{3}}{2}$