# How do you find the exact values of the six trigonometric functions of theta given (24, -7)?

May 28, 2015

I assume that the angle $\theta$ is between the X-axis and the line from the origin through the specified point $\left(24 , - 7\right)$ as in the diagram below:

$\sin \left(\theta\right) = - \frac{7}{24}$

$\cos \left(\theta\right) = \frac{24}{25}$

$\tan \left(\theta\right) = - \frac{7}{24}$

$\csc \left(\theta\right) = - \frac{24}{7}$

$\sec \left(\theta\right) = \frac{25}{24}$

$\cot \left(\theta\right) = - \frac{24}{7}$