Question

If $0<x<\frac{\pi }{2}$ and $\cos x=0.34$, find the value of $\sin \left(\frac{x}{2}\right)$.

• A. $0.574$
• B. $0.733$
• C. $0.819$
• D. $0.917$
• E. $0.941$

Answer 1

The correct option is A $0.574$

Given, $\cos x=0.34$
We know $\cos x=1-2{\sin }^2\frac{x}{2}=0.34$
$\Rightarrow 2{\sin }^2\frac{x}{2}=0.66$
$\Rightarrow {\sin }^2\frac{x}{2}=0.33$

$\Rightarrow \sin \frac{x}{2}=\sqrt{0.33}=0.574$