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33 votes
33 votes
If the value of tan θ<0 and sin θ>0 , then the angle θ must lie in which quadrant?

User JLTChiu
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1 Answer

21 votes
21 votes

Given:


\tan \theta<0\text{ and }\sin \theta>0
\text{ we know that }\tan \theta=(\sin \theta)/(\cos \theta)\text{.}
\text{ Replace tan}\theta=(\sin \theta)/(\cos \theta)\text{ in tan}\theta<0\text{ as follows.}
(\sin \theta)/(\cos \theta)<0
\text{Multiply cos}\theta\text{ on both sides.}


(\sin\theta)/(\cos\theta)*\cos \theta<0*\cos \theta
\sin \theta<0
\text{But given that sin}\theta>0

hence sine value should be equal to 0.


\sin \theta=0
\theta=\sin ^(-1)0
\theta=\sin ^(-1)\sin (n\pi)
\theta=n\pi\text{ where n is integer.}

User Shimon Wiener
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3.1k points