Answer
$tan~\theta=-\frac{\sqrt {11}}{5}$
$cot~\theta=-\frac{5\sqrt {11}}{11}$
$csc~\theta=-\frac{6\sqrt {11}}{11}$
$cos~\theta=\frac{5}{6}$
$sin~\theta=-\frac{\sqrt {11}}{6}$
Work Step by Step
$sec^2\theta=1+tan^2\theta$
$tan^2\theta=(\frac{6}{5})^2-1=\frac{11}{25}$
$tan~\theta=-\frac{\sqrt {11}}{5}$
$cot~\theta=\frac{1}{tan~\theta}=-\frac{5}{\sqrt {11}}=-\frac{5\sqrt {11}}{11}$
$csc^2\theta=cot^2\theta+1=\frac{25}{11}+1=\frac{36}{11}$
$csc~\theta=-\frac{6}{\sqrt {11}}=-\frac{6\sqrt {11}}{11}$
$cos~\theta=\frac{1}{sec~\theta}=\frac{1}{\frac{6}{5}}=\frac{5}{6}$
$sin~\theta=\frac{1}{csc~\theta}=\frac{1}{-\frac{6}{\sqrt {11}}}=-\frac{\sqrt {11}}{6}$
