# Thread: Finding the equation for the normal

1. ## Finding the equation for the normal

Find the equation of the normal to y = cosec(2x) at the point where x = pi/4.

Differentiating cosec(2x) = -2cot(2x)cosec(2x)
At x = pi/4, dy/dx = -2cot(pi/2)cosec(pi/2)

I am unable to get a value for the dy/dx of the tangent since cot(pi/2) is undefined! How should I continue or did I make any mistakes?

Thank you very much!

2. ## Re: Finding the equation for the normal

The cotangent function is not undefined there. Look at it again.

3. ## Re: Finding the equation for the normal

Originally Posted by Tutu
Find the equation of the normal to y = cosec(2x) at the point where x = pi/4.

Differentiating cosec(2x) = -2cot(2x)cosec(2x)
At x = pi/4, dy/dx = -2cot(pi/2)cosec(pi/2)

I am unable to get a value for the dy/dx of the tangent since cot(pi/2) is undefined! How should I continue or did I make any mistakes?

Thank you very much!
Surely if \displaystyle \begin{align*} \cot{\left( \frac{\pi}{2} \right)} \end{align*} is undefined, then the tangent line is vertical. So wouldn't the normal line have to be horizontal?

4. ## Re: Finding the equation for the normal

Hi thanks! But aren't co tangents undefined? I cannot find q value, it keeps coming back undefined..unless I type the whole cot and cosec in?