Answer
$\cos\theta=\frac{\sqrt {5}}{8}$
$\sec\theta=\frac{8\sqrt {5}}{5}$
$ \sin\theta=-\frac{\sqrt{ 59}}{8}$
$\csc\theta=-\frac{8\sqrt {59}}{59}$
$\tan\theta=-\frac{\sqrt {295}}{5}$
$\cot\theta=-\frac{\sqrt {295}}{59}$
Work Step by Step
$\cos\theta=\frac{\sqrt {5}}{8}$
$\sec\theta=\frac{1}{\cos\theta}=\frac{8}{\sqrt 5}=\frac{8\sqrt {5}}{5}$
$\sin^{2}\theta=1-\cos^{2}\theta=1-(\frac{\sqrt {5}}{8})^{2}=\frac{59}{64}$
$\implies \sin\theta=\pm\sqrt {\frac{59}{64}}=-\frac{\sqrt{ 59}}{8}$ ($\sin\theta\lt0$ as $\tan\theta\lt0$ and $\cos\theta\gt0$)
$\csc\theta=\frac{1}{\sin\theta}=-\frac{8}{\sqrt {59}}=-\frac{8\sqrt {59}}{59}$
$\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{-\frac{\sqrt {59}}{8}}{\frac{\sqrt 5}{8}}=-\frac{\sqrt {59}}{\sqrt {5}}=-\frac{\sqrt {295}}{5}$
$\cot\theta=\frac{1}{\tan\theta}=-\frac{\sqrt 5}{\sqrt {59}}=-\frac{\sqrt {295}}{59}$
