Question

If $\sin \theta =\frac{\sqrt{3}}{2}$, where $\theta$ is an acute angle, then find the value of $\cos \theta$.

Answer 1

Given, $\sin \theta =\frac{\sqrt{3}}{2}$
But, $\cos \theta =\sqrt{1-{\sin }^2\theta }$
$\Rightarrow \cos \theta =\sqrt{1-\frac{3}{4}}$
$\Rightarrow \cos \theta =\sqrt{\frac{1}{4}}$
$\Rightarrow \cos \theta =\frac{1}{2}$