Question

If $\sin \theta =\frac{5}{13}$, where $\theta$ is acute angle, find the value of $\cos \theta$.

Answer 1

Given, $\sin \theta =\frac{5}{13}$

$\cos \theta =\sqrt{1-{\sin }^2\theta }$

$\Rightarrow \cos \theta =\sqrt{1-\frac{25}{169}}$

$\Rightarrow \cos \theta =\sqrt{\frac{144}{169}}$

$\Rightarrow \cos \theta =\frac{12}{13}$