Question

The principal solution of the equation $\sin x=\frac{1}{2}$ that is less than $\frac{\pi }{2}$ is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$

Answer 1

The correct option is C $\frac{\pi }{6}$

Given equation is:
$\sin x=\frac{1}{2}$
$\Rightarrow \sin x=\sin \frac{\pi }{6}$
Thus, one principal solution of the equation is $\frac{\pi }{6}$

Also, $\sin x=\sin (\pi -x)$
Thus, $\sin \frac{\pi }{6}=\sin (\pi -\frac{\pi }{6})$
Or, $\sin \frac{\pi }{6}=\sin \frac{5\pi }{6}$

Thus, the other prinicipal solution of the equation is $\frac{5\pi }{6}$.

The principal solution which is less than $\frac{\pi }{2}$ is $\frac{\pi }{6}$