# How do you find the values of the six trigonometric functions given tantheta is undefined and pi<=theta<=2pi?

May 22, 2017

See below

#### Explanation:

$\tan \theta = \text{undefined}$ and $\pi \le \theta \le 2 \pi$

$\tan \theta = \sin \frac{\theta}{\cos} \theta$

Since $\tan \theta$ is undefined, $\cos \theta = 0$. Therefore $\theta = \frac{3}{2} \pi$.

$\sin \left(\theta\right) = \sin \left(\frac{3}{2} \pi\right) = - 1$

$\csc \left(\theta\right) = \frac{1}{\sin} \theta = - 1$

$\sec \left(\theta\right) = \frac{1}{\cos} \theta = \text{undefined}$

$\cot \left(\theta\right) = \cos \frac{\theta}{\sin} \theta = 0$