Answer
$\cot\theta=\frac{\sqrt 3}{8}$
$\tan\theta=\frac{8\sqrt 3}{3}$
$\sec\theta=\frac{\sqrt {201}}{3}$
$\cos\theta=\frac{\sqrt {201}}{67}$
$\sin\theta=\frac{8\sqrt {67}}{67}$
$\csc\theta=\frac{\sqrt {67}}{8}$
Work Step by Step
$\cot\theta=\frac{\sqrt 3}{8}$
$\tan\theta=\frac{1}{\cot\theta}=\frac{8}{\sqrt {3}}=\frac{8\sqrt 3}{3}$
$\sec^{2}\theta=1+\tan^{2}\theta=1+\frac{64}{3}=\frac{67}{3}$
$\implies \sec\theta=\pm \frac{\sqrt {67}}{\sqrt 3}=\pm\frac{\sqrt {67\times3}}{3}$
$\sec\theta$ is positive in the first quadrant.
$\implies \sec\theta=\frac{\sqrt {201}}{3}$
$\cos\theta=\frac{1}{\sec\theta}=\frac{\sqrt 3}{\sqrt{ 67}}=\frac{\sqrt {201}}{67}$
$\sin\theta=\tan\theta\times\cos\theta=\frac{8}{\sqrt 3}\times\frac{\sqrt 3}{\sqrt {67}}=\frac{8\sqrt {67}}{67}$
$\csc\theta=\frac{1}{\sin\theta}=\frac{\sqrt {67}}{8}$
