How do you find the value of $cot 90$ ?

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Answer 1 · 2015-07-11T23:40:19

$cot(90)=0$

Recall that $cot(theta)=1/tan(theta)$

and that $tan(theta)=sin(theta)/cos(theta)$

So,

$cot(theta)=1/tan(theta)=1/(sin(theta)/cos(theta))=cos(theta)/sin(theta)$

Now, let's just put in 90 degrees for $theta$

$cot(theta)=cos(theta)/sin(theta)$

$cot(90)=cos(90)/sin(90)$

Recall, from the unit circle (below) that $sin(90)=1$ and $cos(90)=0$ :

enter image source here

So,

$cot(90)=cos(90)/sin(90)$

$cot(90)=0/1 =0$

How do you find the value of cot 90cot 90?