# How do you find the value of cot((3pi)/2)?

Feb 8, 2016

$\cot \left(\frac{3 \pi}{2}\right) = 0$

#### Explanation:

As you know, $\cot \left(x\right) = \cos \frac{x}{\sin} \left(x\right)$.

Thus, you can compute the value of

$\cos \frac{\frac{3 \pi}{2}}{\sin} \left(\frac{3 \pi}{2}\right)$

Let's take a look at the $\sin$ and $\cos$ functions:
As you can see, $\sin \left(\frac{3 \pi}{2}\right) = - 1$ and $\cos \left(\frac{3 \pi}{2}\right) = 0$.
$\cot \left(\frac{3 \pi}{2}\right) = \frac{0}{- 1} = 0$.