Question

If tan $\theta$ = $\frac{\sqrt{7}}{2}$, and cos $\theta$ = $\frac{2}{\sqrt{11}}$ find sin $\theta$.

Answer 1

(ii)
$$\begin{gathered} \mathrm{Given}:\tan \mathrm{\theta }=\frac{\sqrt{7}}{2}\mathrm{and}\cos \mathrm{\theta }=\frac{2}{\sqrt{11}} \\ \mathrm{We}\mathrm{have}\tan \mathrm{\theta }=\frac{\sin \mathrm{\theta }}{\cos \mathrm{\theta }} \\ \Rightarrow \tan \mathrm{\theta }\times \cos \mathrm{\theta }=\sin \mathrm{\theta } \\ \Rightarrow \frac{\sqrt{7}}{2}\times \frac{2}{\sqrt{11}}=\sin \mathrm{\theta } \\ \Rightarrow \frac{\sqrt{7}}{\sqrt{11}}=\sin \mathrm{\theta } \end{gathered}$$