# 4. If the cosecant of a fourth quadrant angle is –π/e, what is its cosine? Thanks

Feb 3, 2018

$\cos \left(\theta\right) = \frac{\sqrt{{\pi}^{2} - {e}^{2}}}{\pi}$

#### Explanation:

Since $\csc \left(\theta\right) = - \frac{\pi}{e}$, we can use Pythagorean theorem to find the missing side in a $e , x , \pi$ triangle:

$x = \sqrt{{\pi}^{2} - {e}^{2}}$

So the ordered pair through which the angle passes is $\left(\sqrt{{\pi}^{2} - {e}^{2}} , - e\right)$.

$\cos \left(\theta\right) = \frac{x}{r} = \frac{\sqrt{{\pi}^{2} - {e}^{2}}}{\pi}$