# What does tan 0 equal?

Oct 21, 2015

$\tan \left(0\right)$ is "undefined"

#### Explanation:

In general based on a triangle with adjacent side on the X-axis and a hypotenuse extending from the origin to a point on the unit circle $\tan$ is defined as
$\textcolor{w h i t e}{\text{XXX")tan(theta) = ("opposite side")/("adjacent side}}$

As $\theta \rightarrow 0$
the $\text{adjacent side} \rightarrow 0$
so the definition of $\tan \left(0\right)$ becomes an attempt to divide by $0$,
an operation which is "undefined"