The cotangent function is defined as the ratio between cosine and sine of a given angle, i.e.
[tex] \cot(x) = \frac{\cos(x)}{\sin(x)} [/tex]
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:
[tex] \sin(90^\circ) = 1 [/tex], so the cotangent is defined here
[tex] \sin(180^\circ) = 0 [/tex], so the cotangent is not defined here
[tex] \sin(270^\circ) = -1 [/tex], so the cotangent is defined here
[tex] \sin(450^\circ) = \sin(360^\circ+90^\circ)=\sin(90^\circ) = 1 [/tex], so the cotangent is defined here
