Question

If $\tan \theta =\frac{1}{\sqrt{3}}$ and $\cos \theta =\frac{\sqrt{3}}{2}$ then the value of $\sin \theta$ is

• A. $\sqrt{3}$
• B. $\frac{1}{2}$
• C. $\frac{2}{\sqrt{3}}$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{1}{2}$

By using $\tan \theta =\frac{\sin \theta }{\cos \theta }$

We can write $\sin \theta =\tan \theta \times \cos \theta$

So $\sin \theta =\frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{2}$

$\sin \theta =\frac{1}{2}$