Question

For which value of theta is cot (theta) undefined?

Answer 1

The answer is B. 180

Answer 2

The cotangent function is defined as the ratio between cosine and sine of a given angle, i.e.

$\cot(x) = \frac{\cos(x)}{\sin(x)}$

Since you can't have zero at the denominator, the cotangent function is not defined when the sine is zero.

Let's look at your option:

$\sin(90^\circ) = 1$, so the cotangent is defined here

$\sin(180^\circ) = 0$, so the cotangent is not defined here

$\sin(270^\circ) = -1$, so the cotangent is defined here

$\sin(450^\circ) = \sin(360^\circ+90^\circ)=\sin(90^\circ) = 1$, so the cotangent is defined here