# Convert from polar to rectangular

• July 24th 2012, 08:50 AM
Greymalkin
Convert from polar to rectangular
r= $sec^2{\theta\over 2}$

Book answer is: $y^2=-4x+4$
Maybe there is an easier way, but... First express $\sec^2(\theta/2)$ through $\cos\theta$ using the double-angle formula. Then replace r by $\sqrt{x^2+y^2}$ and $\cos\theta$ by $x/\sqrt{x^2+y^2}$ and simplify. It may be necessary to separately check special cases, such as when r = 0.