Question

Is 3pi/2 undefined or is cot -pi/2 undefined?

Answer 1

Try to remember the relationship that tangent and cotangent have to sine and cosine.\[\Large \tan x\quad=\quad\frac{\sin x}{\cos x}\]

The problem is, cos(3pi/2)=0.
That would give us a 0 in the denominator of our fraction, right?
We can't divide by 0 in the land of math!! :O
So yes tan(3pi/2) is undefined.

Answer 2

\[\Large \cot x\quad=\quad \frac{\cos x}{\sin x}\]
Here we only need to worry about the sine function (since that's the one in the denominator).

Answer 3

\[\Large \sin(-\pi/2)=-1\]No problems! :D
So cotangent shouldn't be undefined.