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

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

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Answer 1 · 2015-07-11T23:40:19

$cot (90) = 0$ $cot(90)=0$

Explanation:

Recall that $cot (θ) = \frac{1}{tan (θ)}$ $cot(theta)=1/tan(theta)$

and that $tan (θ) = \frac{sin (θ)}{cos (θ)}$ $tan(theta)=sin(theta)/cos(theta)$

So,

$cot (θ) = \frac{1}{tan (θ)} = \frac{1}{\frac{sin (θ)}{cos (θ)}} = \frac{cos (θ)}{sin (θ)}$ $cot(theta)=1/tan(theta)=1/(sin(theta)/cos(theta))=cos(theta)/sin(theta)$

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

$cot (θ) = \frac{cos (θ)}{sin (θ)}$ $cot(theta)=cos(theta)/sin(theta)$

$cot (90) = \frac{cos (90)}{sin (90)}$ $cot(90)=cos(90)/sin(90)$

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

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So,

$cot (90) = \frac{cos (90)}{sin (90)}$ $cot(90)=cos(90)/sin(90)$

$cot (90) = \frac{0}{1} = 0$ $cot(90)=0/1 =0$

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

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