# If (-4,1) is a point of the terminal side of angle in standard position evaluate all 6 trig functions of pheta in simplest radical form?

Jan 16, 2016

First, find the hypotenuse $h$ ...

#### Explanation:

${h}^{2} = {x}^{2} + {y}^{2}$

${h}^{2} = {\left(- 4\right)}^{2} + {\left(1\right)}^{2} = 17$

$h = \sqrt{17}$

$\sin \theta = \frac{y}{h} = \frac{1}{\sqrt{17}} = \frac{\sqrt{17}}{17}$

$\cos \theta = \frac{x}{h} = \frac{- 4}{\sqrt{17}} = \frac{- 4 \sqrt{17}}{17}$

$\tan \theta = \sin \frac{\theta}{\cos} \theta = - \frac{1}{4}$

The final 3 are simply the reciprocal of the first three , so I'll leave the other 3 for you to solve :)

hope that helped