Answer
$sec~\theta=-\frac{41}{9}$
$cot~\theta=-\frac{9}{40}$
$csc~\theta=\frac{41}{40}$
$cos~\theta=-\frac{9}{41}$
$sin~\theta=\frac{40}{41}$
Work Step by Step
$sec^2\theta=1+tan^2\theta=1+(-\frac{40}{9})^2=\frac{1681}{81}$
$sec~\theta=-\frac{41}{9}~~~~$ $(sin~\theta\gt0$ and $cos~\theta\lt0)$
$cot~\theta=\frac{1}{tan~\theta}=\frac{1}{-\frac{40}{9}}=-\frac{9}{40}$
$csc^2\theta=cot^2\theta+1=(-\frac{9}{40})^2+1=\frac{1681}{1600}$
$csc~\theta=\frac{41}{40}$
$cos~\theta=\frac{1}{sec~\theta}=-\frac{9}{41}$
$sin~\theta=\frac{1}{csc~\theta}=\frac{40}{41}$
