How do you evaluate the expression $cot(-pi)$ ?

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Answer 1 · 2016-09-14T05:07:50

See explanation.

Use $cos (-pi)==1 and sin (-pi)=0$ .

Importantly, cot x is discontinuous at $x=-pi$ .

Let $y = cot x = cos x/sin x, x in Q_2(-pi, -3/2pi)$ , wherein it is

continuous.

As $x to - pi_+$ , the approach to $-pi$ is from higher values in

$Q_2$ , at which $cot x < 0$ , with x in $Q_2$ . So, the limit, through

negative values of cot x = cos x/sin x is $-oo$

In brief, the limit $x to -pi_+$ of cot x is $-oo$

By a similar argument, as $x to -pi_-$ of cot x in $Q_3$ , wherein

$cot x > 0$ , is $oo$ . .

How do you evaluate the expression cot(-pi)cot(-pi)?