If cot θ = 3/4 and the terminal point determined by θ is in quadrant 3, then:

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$\cot(\theta)=\dfrac {\cos(\theta)}{\sin(\theta)}=\dfrac 3 4$

since $\sin^2(\theta)+\cos^2(\theta)=1$ we know that in the first quadrant

$\dfrac {\cos(\theta)}{\sin(\theta)}=\dfrac 3 4 \Rightarrow \cos(\theta)=\dfrac 3 5\mbox{, and }\sin(\theta)=\dfrac 4 5$

but we're in the 3rd quadrant so we have

$\sin(\theta)=-\dfrac 4 5$

$\cos(\theta)=-\dfrac 3 5$

which matches up with answer (b)