Question

If cos $\mathrm{\theta }$ = $\frac{15}{17}$ then find sin $\mathrm{\theta }$

Answer 1

$$\begin{gathered} {\sin }^2\theta +{\cos }^2\theta =1 \\ \Rightarrow {\sin }^2\theta +{\left(\frac{15}{17}\right)}^2=1\left(\cos \theta =\frac{15}{17}\right) \\ \Rightarrow {\sin }^2\theta +\frac{225}{289}=1 \\ \Rightarrow {\sin }^2\theta =1-\frac{225}{289} \\ \Rightarrow {\sin }^2\theta =\frac{289-225}{289}=\frac{64}{289} \end{gathered}$$
$$\begin{gathered} \Rightarrow \sin \theta =\sqrt{\frac{64}{289}}=\sqrt{{\left(\frac{8}{17}\right)}^2} \\ \Rightarrow \sin \theta =\frac{8}{17} \end{gathered}$$
Thus, the value of sinθ is $\frac{{\displaystyle 8}}{17}$.