Question

If $\cos 3x=0$ and $x$ is acute, then find the value of $\sin x$.

Answer 1

Given that, $\cos 3x=0$, where $x$ is acute.

We know that $\cos {90}^o=0$
$\therefore \cos 3x=\cos {90}^o$
$\Rightarrow 3x={90}^o$
Hence, $x={30}^o$
Now, $\sin x=\sin {30}^o=\frac{1}{2}$

Hence, if $\cos 3x=0$ and $x$ is acute, then the value of $\sin x$ is $\frac{1}{2}$.