Question

Are tan 3pi/2 and cot -pi/2 both undefined? If not, how do I tell if one is and one isn't?

Answer 1

\[\tan (3\pi/2)\] is undefined because the value of sin at \[(3\pi/2)\] is -1 but the value of \[(3\pi/2)\] is 0;

Therefore, \[\tan = \sin /\cos = -1/0\] in which any value divide by zero is undefined.

Part 2 of your questions asks if \[\cot (-\pi/2) \] is undefined. Fortunately this is the same place on the unit circle but the value of cot becomes, \[\cot = \cos / \sin \] where we already know cos = 0 and sin = -1, thus \[\cot = 0/-1\].

Understand?

Answer 2

so 0/-1 isnt considered undefined?

Answer 3

No, it is considered 0.