2 Answers

Nikolaus Gradwohl · Answer 1 · 2019-12-10T08:57:41+0000

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

$\cot(x) = (\cos(x))/(\sin(x))$

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

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