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#:

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So,

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

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