Answer
$sin~\theta=-\frac{24}{25}$
$cos~\theta=\frac{7}{25}$
$tan~\theta=-\frac{24}{7}$
$cot~\theta=-\frac{7}{24}$
$sec~\theta=\frac{25}{7}$
$csc~\theta=-\frac{25}{24}$
Work Step by Step
Distance from the origin to the given point:
$d=\sqrt {7^2+(-24)^2}=\sqrt {625}=25$
$sin~\theta=\frac{opp}{hyp}=\frac{-24}{25}=-\frac{24}{25}$
$cos~\theta=\frac{adj}{hyp}=\frac{7}{25}$
$tan~\theta=\frac{opp}{adj}=\frac{-24}{7}=-\frac{24}{7}$
$cot~\theta=\frac{adj}{opp}=\frac{7}{-24}=-\frac{7}{24}$
$sec~\theta=\frac{hyp}{adj}=\frac{25}{7}$
$csc~\theta=\frac{hyp}{opp}=\frac{25}{-24}=-\frac{25}{24}$
