rectangular equation : x^2 - y^2 = 4

use the double angle forumla

i have no idea what to do?

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- May 25th 2009, 09:38 PMtomatoesconverting 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 PMGrandadConverting to a polar equation
Hello tomatoesUsing $\displaystyle x = r\cos\theta, y = r\sin\theta$, we get:

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

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

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

$\displaystyle r^2\cos2\theta = 4$

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

Grandad