Answer
$\cot\theta=-\frac{4}{3},\sec\theta=-\frac{5}{4},\cos\theta=-\frac{4}{5},\sin\theta=\frac{3}{5},\csc\theta=\frac{5}{3}$
Work Step by Step
Since $\tan\theta=-\frac{3}{4}$, we have $\cot\theta=-\frac{4}{3}$
$\sec^{2}\theta=1+\tan^{2}\theta=1+\frac{9}{16}=\frac{25}{16}$
or $\sec\theta=-\frac{5}{4}$ ($\sec\theta$ will be negative since $\theta$ lies in second quadrant)
Then, $\cos\theta=-\frac{4}{5}$
Further, we have
$\sin\theta=\tan\theta\cos\theta=(-\frac{3}{4})\times(-\frac{4}{5})=\frac{3}{5}$
and $\csc\theta=\frac{5}{3}$
