converting rectangular equations into polar form

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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
Grandad

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 $r^2 = 4\sec2\theta$

Grandad

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