Question

Find the principal solutions of the equation $\sin x=\frac{\sqrt{3}}{2}$.

Answer 1

Given: $\sin x=\frac{\sqrt{3}}{2}$

We know: $\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}$
Here $\sin x$ is positive.
$\sin x$ is positive in $1^{st}$ and $2^{nd}$ quadrant.

Value in $1^{st}$ quadrant $=\frac{\pi }{3}$
Value in $2^{nd}$ quarant $=\pi -\frac{\pi }{3}=\frac{2\pi }{3}$
$\therefore$ Principle solutions are $x=\frac{\pi }{3}$ and $\frac{2\pi }{3}$