Answer
$cos~\theta=-\frac{\sqrt {55}}{8}$
$tan~\theta=-\frac{3\sqrt {55}}{55}$
$cot~\theta=-\frac{\sqrt {55}}{3}$
$sec~\theta=-\frac{8\sqrt {55}}{55}$
$csc~\theta=\frac{8}{3}$
Work Step by Step
$sin^\theta+cos^2\theta=1$
$(\frac{3}{8})^2+cos^2\theta=1$
$cos^2\theta=1-\frac{9}{64}=\frac{55}{64}$
$cos~\theta=-\frac{\sqrt {55}}{8}$
$tan~\theta=\frac{sin~\theta}{cos~\theta}=\frac{\frac{3}{8}}{-\frac{\sqrt {55}}{8}}=-\frac{3\sqrt {55}}{55}$
$cot~\theta=\frac{cos~\theta}{sin~\theta}=\frac{-\frac{\sqrt {55}}{8}}{\frac{3}{8}}=-\frac{\sqrt {55}}{3}$
$sec~\theta=\frac{1}{cos~\theta}=-\frac{8}{\sqrt {55}}=-\frac{8\sqrt {55}}{55}$
$csc~\theta=\frac{1}{sin~\theta}=\frac{8}{3}$
