# $\tan{(90^°)}$ value

The tan value when angle of a right triangle equals to $90^°$ is called tan of angle $90$ degrees. It is mathematically written as $\tan{(90^°)}$ in sexagesimal system.

$\tan{(90^°)} \,=\, \infty$

Mathematically, it is not possible to find the exact value of tangent of angle $90$ degrees because the exact value of $\tan{(90^°)}$ is undefined. So, its value is denoted by infinity symbol.

## Alternative form

The $\tan{(90^°)}$ can be expressed in different ways alternatively. So, it is written as $\tan{\Big(\dfrac{\pi}{2}\Big)}$ in circular system and also written as $\tan{(100^g)}$ in centesimal system.

$(1) \,\,\,$ $\tan{\Big(\dfrac{\pi}{2}\Big)} \,=\, \infty$

$(2) \,\,\,$ $\tan{(100^g)} \,=\, \infty$

### Proof

You just learnt that the exact value of $\tan{(100^g)}$ is undefined and you have to know mathematically how the exact value of $\tan{\Big(\dfrac{\pi}{2}\Big)}$ is infinity in trigonometry.