Answer
$sin~\theta=\frac{opp}{hyp}=\frac{4\sqrt {15}}{17}$
$cos~\theta=\frac{adj}{hyp}=\frac{7}{17}$
$tan~\theta=\frac{opp}{adj}=\frac{4\sqrt {15}}{7}$
$cot~\theta=\frac{adj}{opp}=\frac{7\sqrt {15}}{60}$
$csc~\theta=\frac{hyp}{opp}=\frac{17\sqrt {15}}{60}$
Work Step by Step
$sec~\theta=\frac{hyp}{adj}$
$\frac{17}{7}=\frac{hyp}{adj}$
A right triangle with hypotenuse equal to $17$ and with the adjacent side of $\theta$ equal to $7$ has secant equal to $\frac{17}{7}$
Use the pythagorean theorem to find the opposite side of $\theta$
$17^2=7^2+opp^2$
$opp^2=289-49=240$
$opp=4\sqrt {15}$
$sin~\theta=\frac{opp}{hyp}=\frac{4\sqrt {15}}{17}$
$cos~\theta=\frac{adj}{hyp}=\frac{7}{17}$
$tan~\theta=\frac{opp}{adj}=\frac{4\sqrt {15}}{7}$
$cot~\theta=\frac{adj}{opp}=\frac{7}{4\sqrt {15}}=\frac{7\sqrt {15}}{60}$
$csc~\theta=\frac{hyp}{opp}=\frac{17}{4\sqrt {15}}=\frac{17\sqrt {15}}{60}$
