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Ok so I came across another question. Once again it says let $\cot\theta= 4/3$, with $\cos\theta<0$. Find the remaining trigonometric functions.

By using the identities I got:

\begin{align} \sin\theta&=-3/5 \\ \cos\theta&=-4/5 \\ \tan\theta&=3/4 \\ \csc\theta&=-5/3 \\ \sec\theta&=-5/4 \end{align}

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    Well, to me your answers are correct. In here, $(x,y)=(-4,-3)$ and $\theta$ is in the $III$-quadrant. – 2017-02-06
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    $\cos \theta < 0$ what it means? And also its possible quadrant can be I. – 2017-02-06
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    @KanwaljitSingh In the problem it's given that $\cos \theta<0.$ That means possible quadrants II,III. [then since tangent positive it's quad III]. – 2017-02-06
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    Kanwaljit Singh it isn't possible for the quadrant to be 1 because cos theta < 0 thus it is a negative number and it is only negative im the 2nd a third quadrants but cot is only positive in the 1st and 3rd which is why it is indeed the 3rd quadrant – 2017-02-06
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    Ok I have only doubt in that. – 2017-02-06
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    Then your answer is correct. – 2017-02-06

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