# How do you find the csc of theta if cottheta=1 and pi<theta<3/2pi?

Nov 18, 2016

$\theta = 0$

#### Explanation:

$\cot \theta = 1 \therefore \tan \theta = 1$

$\theta = {\tan}^{-} 1 \left(1\right) = {\left(\frac{\pi}{4}\right)}^{\text{c}}$

However, the given range is between $\pi$ and $\frac{3}{2} \pi$, so this value cannot be used.

In order to find the value permissible within the range, we just need to add $\pi$ to the principle value of $\theta$ to get the actual value needed.

So the value of $\theta$ within the given range is $\frac{5}{4} \pi$

$\csc \theta = \frac{1}{\sin} \theta = \frac{1}{\sin} \left(\frac{5}{4} \pi\right) = \frac{1}{-} 0.707 = - 1.41$