Question:
If $\sin \theta=\frac{1}{2}$ then $\cot \theta=$ ?
(a) $\frac{\sqrt{3}}{2}$
(b) 1
(c) $\sqrt{3}$
(d) $\frac{1}{\sqrt{3}}$
Solution:
Given : $\sin \theta=\frac{1}{2}$
Since, $\sin \theta=\frac{P}{H}$
$\Rightarrow P=1$ and $H=2$
Using Pythagoras theorem,
$P^{2}+B^{2}=H^{2}$
$\Rightarrow 1^{2}+B^{2}=2^{2}$
$\Rightarrow B^{2}=4-1$
$\Rightarrow B^{2}=3$
$\Rightarrow B=\sqrt{3}$
Therefore,
$\cot \theta=\frac{B}{P}=\frac{\sqrt{3}}{1}$
Hence, the correct option is (c).