Question

If $\sin \theta =\frac{1}{2}\cos \theta$, and $0\le \theta \le \frac{\pi }{2}$, then the value of $\frac{1}{2}\sin \theta$ is

• A. $0.22$
• B. $0.25$
• C. $0.45$
• D. $0.50$
• E. $0.75$

Answer 1

The correct option is A $0.22$

Given, $\sin \theta =\frac{1}{2}\cos \theta$

${\sin }^2\theta +{\cos }^2\theta =1$

$\Rightarrow {\sin }^2\theta +4{\sin }^2\theta =1$

$\Rightarrow \sin \theta =\frac{1}{\sqrt{5}}$

$\therefore \frac{1}{2}\sin \theta =\frac{1}{2\sqrt{5}}=0.223$