Question

If sin $\theta$ = $\frac{\sqrt{2}}{3}$, cos $\theta$ = $\frac{1}{3}$ Find tan$\theta$, cot$\theta$, sec $\theta$ and cosec$\theta$.

Answer 1

(i)
$$\begin{gathered} \mathrm{Given}:\sin \mathrm{\theta }=\frac{\sqrt{2}}{3},\mathrm{cos\theta }=\frac{1}{3} \\ \mathrm{Thus},\mathrm{we}\mathrm{know}\mathrm{that}, \\ \mathrm{cosec}\mathrm{\theta }=\frac{1}{\mathrm{sin\theta }}=\frac{3}{\sqrt{2}}, \\ \sec \mathrm{\theta }=\frac{1}{\mathrm{cos\theta }}=\frac{3}{1}=3, \\ \tan \mathrm{\theta }=\frac{\sin \mathrm{\theta }}{\cos \mathrm{\theta }}=\frac{{\displaystyle \frac{\sqrt{2}}{3}}}{{\displaystyle \frac{1}{3}}}=\frac{\sqrt{2}}{1}=\sqrt{2}, \\ \cot \mathrm{\theta }=\frac{1}{\tan \mathrm{\theta }}=\frac{1}{\sqrt{2}} \end{gathered}$$