Question

If $\cos (-{840}^o)=-\frac{1}{2}$ then find the value of $\sin (-{840}^o)$

Answer 1

$-{840}^0=-{360}^0\times 2-{120}^0$

${360}^0⟹0^0$

$⟹-{840}^0=-{120}^0=-{180}^0+{60}^0$

$\cos (-180+60)=-\cos \left(60\right)=-\frac{1}{2}$

$\sin (-840)=sin(-180+60)=-\sin 60=-\frac{\sqrt{3}}{2}$