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If $\sin \theta=-\frac{1}{\sqrt{2}}$ and $\tan \theta=1$, then $\theta$ lies in which quadrant
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Verified Answer
The correct answer is:
Third
$\begin{aligned}
\sin \theta=-\frac{1}{\sqrt{2}} \text { and } \tan \theta & =1 \\
\Rightarrow \sin \theta & =\sin 225^{\circ} \Rightarrow \theta=225^{\circ}
\end{aligned}$
Since $\sin \theta$ is $-v e$ and $\tan \theta$ is $+v e$ in third quadrant.
\sin \theta=-\frac{1}{\sqrt{2}} \text { and } \tan \theta & =1 \\
\Rightarrow \sin \theta & =\sin 225^{\circ} \Rightarrow \theta=225^{\circ}
\end{aligned}$
Since $\sin \theta$ is $-v e$ and $\tan \theta$ is $+v e$ in third quadrant.
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