Question

If ${\sin }^2\theta -\sin \theta -2=0$, then which of the following can be the value of $\theta$ ?

• A. $\frac{3\pi }{2}$
• B. $\frac{9\pi }{2}$
• C. $\frac{5\pi }{2}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is A $\frac{3\pi }{2}$

Given that ${\sin }^2\theta -\sin \theta -2=0$
$\Rightarrow (\sin \theta -2)(\sin \theta +1)=0$
$\Rightarrow \sin \theta =2\text{or}\sin \theta =-1$
But $\sin \theta$ cannot be equal to $2$.
$\Rightarrow \sin \theta =-1$

If $\sin \theta =-1$, then the general solution is
$\theta =(4n-1)\frac{\pi }{2};n\in Z$
$\therefore$ the solution satisfying the options is $\frac{3\pi }{2}.$