Question

(i) If sin 0 $\frac{2}{7}$, find cosec 0
(ii) If tan 0 = $\frac{2}{5}$, find cot 0.

Answer 1

(i)
$$\begin{gathered} \mathrm{Given}, \\ \sin \mathrm{\theta }=\frac{2}{7} \\ \mathrm{We}\mathrm{have}\mathrm{cosec}\mathrm{\theta }=\frac{1}{\sin \mathrm{\theta }} \\ =\frac{1}{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$7$}\right.}}=\frac{7}{2} \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{Given}, \\ \tan \mathrm{\theta }=\frac{2}{5} \\ \mathrm{We}\mathrm{have}\cot \mathrm{\theta }=\frac{1}{\tan \mathrm{\theta }} \\ =\frac{1}{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}}=\frac{5}{2} \end{gathered}$$