# Rectangular to Polar Form?

• May 26th 2010, 12:14 PM
iluvmathbutitshard
Rectangular to Polar Form?
How do I convert y = x^2 to polar form?

Thank you, I really appreciate it.
• May 26th 2010, 12:51 PM
masters
Quote:

Originally Posted by iluvmathbutitshard
How do I convert y = x^2 to polar form?

Thank you, I really appreciate it.

Hi iluvmathbutitshard,

Convert $y=x^2$ into polar form.

In this case there really isn’t much to do other than plugging in the formulas for x and y.

$x=r\cos\theta \:\:and\:\:y=r\sin \theta$

$r\sin \theta=(r\cos \theta)^2$

$r^2 \cos^2 \theta=r\sin \theta$

$r\cos^2 \theta=\sin \theta$

$r=\frac{\sin \theta}{\cos^2 \theta}$
• May 26th 2010, 12:57 PM
iluvmathbutitshard
Thank you for answering. This is actually the answer I got, but does it translate into a different identity? Because the choices I have been given are:
r = cot(theta) csc(theta)
r = tan(theta) sec(theta)
r = tan(theta)
r = cot(theta)
• May 26th 2010, 01:20 PM
masters
Quote:

Originally Posted by iluvmathbutitshard
Thank you for answering. This is actually the answer I got, but does it translate into a different identity? Because the choices I have been given are:
r = cot(theta) csc(theta)
r = tan(theta) sec(theta)
r = tan(theta)
r = cot(theta)

Yes.

$r=\frac{\sin \theta}{\cos^2 \theta} \Longrightarrow \frac{\sin \theta}{\cos \theta}\cdot \frac{1}{\cos \theta}={\color{red}\tan \theta \sec \theta}$