# Math Help - cot(x) = 0, find x

1. ## cot(x) = 0, find x

Okay, so I know that the tan(0 deg) and tan(180 deg) (or 0 rad and pi rads) are both 0, so wouldn't the cot of those be undefined since it's the reciprocal of the tan? The answer says pi/2 though.

2. ## Re: cot(x) = 0, find x

Originally Posted by daigo
Okay, so I know that the tan(90 deg) and tan(270 deg) (or pi/2 and 3pi/4 rads) are both 0, so wouldn't the cot of those be undefined since it's the reciprocal of the tan? The answer says pi/2 though.
\displaystyle \begin{align*} \cot{x} &= 0 \\ \frac{\cos{x}}{\sin{x}} &= 0 \\ \cos{x} &= 0 \\ x &= \frac{\pi}{2} + n\pi, n \in \mathbf{Z} \end{align*}

3. ## Re: cot(x) = 0, find x

in other words, the places where cot(x) = 0 are the places where tan(x) are undefined.