Answer
$sin~\theta=\frac{opp}{hyp}=\frac{\sqrt {10}}{10}$
$cos~\theta=\frac{adj}{hyp}=\frac{3\sqrt {10}}{10}$
$tan~\theta=\frac{opp}{adj}=\frac{1}{3}$
$csc~\theta=\frac{hyp}{opp}=\sqrt {10}$
$sec~\theta=\frac{hyp}{adj}=\frac{\sqrt {10}}{3}$
Work Step by Step
$cot~\theta=\frac{adj}{opp}$
$3=\frac{adj}{opp}$
Use the pythagorean theorem to find the hypotenuse.
$hyp^2=1^2+3^2$
$hyp^2=1+9=10$
$hyp=\sqrt {10}$
$sin~\theta=\frac{opp}{hyp}=\frac{1}{\sqrt {10}}=\frac{\sqrt {10}}{10}$
$cos~\theta=\frac{adj}{hyp}=\frac{3}{\sqrt {10}}=\frac{3\sqrt {10}}{10}$
$tan~\theta=\frac{opp}{adj}=\frac{1}{3}$
$csc~\theta=\frac{hyp}{opp}=\frac{\sqrt {10}}{1}=\sqrt {10}$
$sec~\theta=\frac{hyp}{adj}=\frac{\sqrt {10}}{3}$
