# How do you determine the values of the six trigonometric functions of the angle if the point (-3, 4) is a point on the terminal side of an angle in standard position?

Nov 20, 2014

Given: $\left\{\begin{matrix}\left(x \text{} y\right) = \left(- 3 4\right) \\ r = \sqrt{{\left(- 3\right)}^{2} + {4}^{2}} = 5\end{matrix}\right.$

$\sin \theta = \frac{y}{r} = \frac{4}{5}$

$\cos \theta = \frac{x}{r} = - \frac{3}{5}$

$\tan \theta = \frac{y}{x} = - \frac{4}{3}$

$\csc \theta = \frac{r}{y} = \frac{5}{4}$

$\sec \theta = \frac{r}{x} = - \frac{5}{3}$

$\cot \theta = \frac{x}{y} = - \frac{3}{4}$

I hope that this was helpful.