Find the principle and general solutions of `sin x =-sqrt3/2`

Explanation

We have .sin x=-(sqrt(3))/(2)=-sin (pi)/(3)=sin (pi+(pi)/(3))=sin (4 pi)/(3).

Hence .sin x=sin (4 pi)/(3)., which gives

.(x)=(n) pi+(-1)^((n)) (4 pi)/(3)., where .(n) in (Z).