# Math Help - Polar Equation to Coordinate

1. ## Polar Equation to Coordinate

Hello. I don't have the slightest idea of how to change this equation:
r = 3cos(2q) (q being an angle, call it theta, or whatever) to coordinate form.

i know that x=r cosq and y=r sinq but how i can use this to convert to the coordinate form?

thank you. if you can please show me a step by step to undersand it well.

2. Hello, guidol92!

You need a trig identity like: . $\cos2\theta \:=\:\cos^2\theta - \sin^2\theta$

Write in rectangular coordinates: . $
r \:=\:3\cos(2\theta)$
Multiply by $r^2\!:\;\;\;r^3 \:=\:3r^2\cos2\theta \;=\;3r^2(\cos^2\theta-\sin^2\theta ) \;=\;3\bigg[r^2\cos^2\theta - r^2\sin^2\theta\bigg]$

. . . . . . . . . . $r^3 \;=\;3\bigg[(r\cos\theta)^2 - (r\sin\theta)^2\bigg]$

. . . . $(\sqrt{x^2+y^2})^3 \;=\;3(x^2 - y^2)
$

. . . . . . $(x^2+y^2)^3 \;=\;9(x^2-y^2)^2$