converting rectangular equations into polar form

• May 25th 2009, 09:38 PM
tomatoes
converting rectangular equations into polar form
rectangular equation : x^2 - y^2 = 4

use the double angle forumla

i have no idea what to do?
• May 25th 2009, 10:16 PM
Converting to a polar equation
Hello tomatoes
Quote:

Originally Posted by tomatoes
rectangular equation : x^2 - y^2 = 4

use the double angle forumla

i have no idea what to do?

Using $x = r\cos\theta, y = r\sin\theta$, we get:

$r^2\cos^2\theta - r^2\sin^2\theta = 4$

$\Rightarrow r^2(\cos^2\theta - \sin^2\theta) = 4$

But, using the double-angle formula, $\cos^2\theta - \sin^2\theta = \cos2\theta$, this becomes

$r^2\cos2\theta = 4$

or $r^2 = 4\sec2\theta$