Question

If $\sin \mathrm{\theta }=\frac{1}{2}\mathrm{then}\cot \mathrm{\theta }=?$
(a) $\frac{\sqrt{3}}{2}$

(b) 1

(c) $\sqrt{3}$

(d) $\frac{1}{\sqrt{3}}$

Answer 1

$$\begin{gathered} \mathrm{Given}:\sin \theta =\frac{1}{2} \\ \mathrm{Since},\sin \theta =\frac{P}{H} \\ \Rightarrow P=1\mathrm{and}H=2 \\ \mathrm{Using}\mathrm{Pythagoras}\mathrm{theorem}, \\ {P}^2+B^2=H^2 \\ \Rightarrow 1^2+B^2=2^2 \\ \Rightarrow B^2=4-1 \\ \Rightarrow B^2=3 \\ \Rightarrow B=\sqrt{3} \\ \mathrm{Therefore}, \\ \cot \theta =\frac{B}{P}=\frac{\sqrt{3}}{1} \end{gathered}$$

Hence, the correct option is (c).