# What does tan pi/2 equal?

Sep 7, 2015

$\tan \left(\frac{\pi}{2}\right)$ is not defined.

#### Explanation:

You can find it out whwn you try to calculate it using identity

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

For $x = \frac{\pi}{2}$ the denominator of this expression is zero, so it cannot be calculated.

Sep 7, 2015

$\tan \left(\frac{\pi}{2}\right)$ is undefined
In general the $\tan$ of an angle based on the unit circle in standard position is defined to be $\frac{y}{x}$ where $\left(x , y\right)$ is the coordinate of the terminal point of the radial arm.
...but at $\frac{\pi}{2}$
$\textcolor{w h i t e}{\text{XXX}} x = 0$
and division by $0$ is undefined.