Question

If $\mathrm{sin\theta }=\frac{11}{61}$, find the values of cosθ using trigonometric identity.

Answer 1

We have,

$$\begin{gathered} {\sin }^2\theta +{\cos }^2\theta =1 \\ \Rightarrow {\cos }^2\theta =1-{\sin }^2\theta \\ \Rightarrow {\cos }^2\theta =1-{\left(\frac{11}{61}\right)}^2 \\ \Rightarrow {\cos }^2\theta =1-\frac{121}{3721}=\frac{3721-121}{3721}=\frac{3600}{3721} \end{gathered}$$
$\Rightarrow \cos \theta =\sqrt{{\left(\frac{60}{61}\right)}^2}=\frac{60}{61}$

Thus, the value of cosθ is $\frac{60}{61}$.