# How do you tell whether the value of tan 90 degrees is positive, negative, zero or undefined?

Mar 7, 2018

Undefined

#### Explanation:

We have:

$\tan {90}^{\circ}$

Know that, $\tan \theta = \frac{\sin \theta}{\cos \theta}$

So here, we get

$\tan {90}^{\circ} = \frac{\sin {90}^{\circ}}{\cos {90}^{\circ}}$

Looking at the trigonometric table, we see that $\sin {90}^{\circ} = 1 , \cos {90}^{\circ} = 0$.

Therefore,

$\tan {90}^{\circ} = \frac{1}{0}$

Since anything divided by $0$ (except $0$ itself) is considered to be undefined, we get that $\tan {90}^{\circ}$ is undefined as well.