Question

If $tan\theta =3$ 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

Answer: (C)

Given, $tan\theta =\frac{3}{1}$
$\therefore A{C}^2=A{B}^2+B{C}^2=1+9=10$
$\Rightarrow AC\pm \sqrt{10}$
$\Rightarrow sin\theta =\frac{-3}{\sqrt{10}}$
($\because \theta$ lies in III quadrant, so $sin\theta$ will be negative)