Question

The general solution for $\sin x=\frac{\sqrt{3}}{2}$ is given as

• A. $2n\pi +\frac{\pi }{3}$
• B. $2n\pi -\frac{\pi }{3}$
• C. $n\pi +(-1{)}^n\frac{\pi }{3}$
• D. $2n\pi +(-1{)}^n\frac{\pi }{3}$

Answer 1

The correct option is C $n\pi +(-1{)}^n\frac{\pi }{3}$

We know that the general solution for the equation
$\sin x=\sin \alpha \forall \alpha \in \left[\begin{array}{c}-\frac{\pi }{2},\frac{\pi }{2}\end{array}\right]$ is given by
$x=n\pi +(-1{)}^n\alpha$ where $n$ is an integer.
Here, we are given $\sin x=\frac{\sqrt{3}}{2}$
$\Rightarrow \sin x=\sin \frac{\pi }{3}$
Therefor, the general solution will be,
$x=n\pi +(-1{)}^n\frac{\pi }{3}$