# Math Help - why is cot of 90= 0

1. ## why is cot of 90= 0

well? since tan90 is undefined as well is sec90... how does cot90=0

2. Originally Posted by requal
well? since tan90 is undefined as well is sec90... how does cot90=0
Well, there is another way of defining cot :
$\cot(x)=\frac{1}{\tan(x)}=\frac{1}{\frac{\sin(x)}{ \cos(x)}}=\frac{\cos(x)}{\sin(x)}$
and you can compute this for x=90.

3. Draw several right triangles with one angle 90 degrees (of course) and another angle close to 90 degrees, keeping the hypotenuse of constant length. $cos(\theta)$ is "near side over hypotenuse". As $\theta$ approaches 90 degrees, the "near" gets shorter and shorter: $cos(\theta)$ goes to 0.

As to your refernce to tangent and secant: both of those have cosine in the [b]denominator[b] while the numerator is 1: in a limiting sense, 1/0= infinity.