Question

If $\sin \theta =-\frac{1}{\sqrt{2}}$ and $\tan \theta =1,$ then $\theta$ lies in the quadrant.

• A. first
• B. second
• C. third
• D. fourth

Answer 1

The correct option is C third

Given $\sin \theta =-\frac{1}{\sqrt{2}}$ and $\tan \theta =1$

$\sin \theta$ is negative and $\tan \theta$ is positive.

$\sin \theta$ is negative either in third or fourth quadrant.

It is also given $\tan \theta$ is positive. In third quadrant $\tan \theta$ is positive while in fourth quadrant $\tan \theta$ is negative.

So, $\theta$ should lie in third quadrant.