Question

$\tan \theta =3$ and $\theta$ lies in third quadrant, then the value of $\sin \theta$ is

• A. $\frac{1}{\sqrt{10}}$
• B. $-\frac{1}{\sqrt{10}}$
• C. $\frac{-3}{\sqrt{10}}$
• D. $\frac{3}{\sqrt{10}}$

Answer 1

The correct option is C $\frac{-3}{\sqrt{10}}$

$tan\theta =\frac{3}{1}$

$sin\theta =\frac{3}{\sqrt{3^2+1^2}}$

(In third Quadrant $sin\theta$ is -ve)

$sin\theta =\frac{-3}{\sqrt{10}}$