# Finding the equation for the normal

• Nov 29th 2012, 07:55 PM
Tutu
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!
• Nov 29th 2012, 08:01 PM
MarkFL
Re: Finding the equation for the normal
The cotangent function is not undefined there. Look at it again. :)
• Nov 29th 2012, 08:02 PM
Prove It
Re: Finding the equation for the normal
Quote:

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?
• Dec 5th 2012, 08:27 AM
Tutu
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?