Question

If $\sin \left(\theta \right)=-\frac{1}{\sqrt{2}}$ and $\tan \left(\theta \right)=1$, then $\left(\theta \right)$ lies in which quadrant $?$

• A. First
• B. Second
• C. Third
• D. Fourth

Answer 1

The correct option is C

Third

Solving $\left(\theta \right)$:

$\sin \left(\theta \right)=-\frac{1}{\sqrt{2}}$ and

$\tan \left(\theta \right)=1$

From given term , we know that

$\sin \left(\theta \right)$ is negative in quadrant $\left(3\right)$ and quadrant $\left(4\right)$

And

$\tan \left(\theta \right)$ is positive in quadrant $\left(1\right)$ and quadrant $\left(3\right)$

So , from above both statements

Quadrant $\left(3\right)$ is common ,

$\therefore$ $\left(\theta \right)$ lies in quadrant $\left(3\right)$.

Hence , option (C) is correct.