Answer
$sin~\theta=\frac{opp}{hyp}=\frac{\sqrt {11}}{6}$
$cos~\theta=\frac{adj}{hyp}=\frac{5}{6}$
$tan~\theta=\frac{opp}{adj}=\frac{\sqrt {11}}{5}$
$cot~\theta=\frac{adj}{opp}=\frac{5\sqrt {11}}{11}$
$csc~\theta=\frac{hyp}{opp}=\frac{6\sqrt {11}}{11}$
Work Step by Step
$sec~\theta=\frac{hyp}{adj}$
$\frac{6}{5}=\frac{hyp}{adj}$
Use the pythagorean theorem to find the opposite side of $\theta$
$6^2=5^2+opp^2$
$opp^2=36-25=11$
$opp=\sqrt {11}$
$sin~\theta=\frac{opp}{hyp}=\frac{\sqrt {11}}{6}$
$cos~\theta=\frac{adj}{hyp}=\frac{5}{6}$
$tan~\theta=\frac{opp}{adj}=\frac{\sqrt {11}}{5}$
$cot~\theta=\frac{adj}{opp}=\frac{5}{\sqrt {11}}=\frac{5\sqrt {11}}{11}$
$csc~\theta=\frac{hyp}{opp}=\frac{6}{\sqrt {11}}=\frac{6\sqrt {11}}{11}$
