Answer
$cos~\theta = \frac{24}{25}$
$sin~\theta = -\frac{7}{25}$
$tan~\theta = -\frac{7}{24}$
$sec~\theta = \frac{25}{24}$
$csc~\theta = -\frac{25}{7}$
$cot~\theta = -\frac{24}{7}$
Work Step by Step
Since $\theta$ is in quadrant IV, $sin ~\theta$ is negative, $cos~\theta$ is positive, and $tan~\theta$ is negative.
$cos~\theta = \frac{24}{25}$
$sin^2~\theta+cos^2~\theta = 1$
$sin^2~\theta = 1 - cos^2~\theta$
$sin^2~\theta = 1 - (\frac{24}{25})^2$
$sin~\theta = -\sqrt{1 - (\frac{24}{25})^2}$
$sin~\theta = -\frac{7}{25}$
$tan~\theta = \frac{sin~\theta}{cos~\theta}$
$tan~\theta = \frac{-\frac{7}{25}}{\frac{24}{25}}$
$tan~\theta = -\frac{7}{24}$
$sec~\theta = \frac{1}{cos~\theta}$
$sec~\theta = \frac{1}{(24/25)}$
$sec~\theta = \frac{25}{24}$
$csc~\theta = \frac{1}{sin~\theta}$
$csc~\theta = \frac{1}{(-7/25)}$
$csc~\theta = -\frac{25}{7}$
$cot~\theta = \frac{1}{tan~\theta}$
$cot~\theta = \frac{1}{(-7/24)}$
$cot~\theta = -\frac{24}{7}$
