# Converting from a polar equation to a cartesian equation

• Dec 1st 2009, 02:54 PM
c.chav506
Converting from a polar equation to a cartesian equation
Hey guys here’s the equation that I had to convert from polar (r, theta) to Cartesian (x,y)…

r = 4 sin (theta)

and this is what I got…

(x^2 +y^2) ^(5/2) = 4(x^4)(y) - 4(x)(y^3)

Can someone check to see if I’m correct?
• Dec 1st 2009, 03:05 PM
qmech
$\displaystyle r = 4 sin \theta$

Multiply both sides by r
$\displaystyle r^2 = 4 r sin \theta$

to get
$\displaystyle x^2 + y^2 = 4 y$
• Dec 1st 2009, 03:10 PM
c.chav506
whoops...
im so sorry qmech... the actual question was

r = sin 4(theta)

sorry for the inconvenience
• Dec 1st 2009, 03:32 PM
qmech
$\displaystyle r = sin ( 4 \theta )$

$\displaystyle r = 2 sin ( 2 \theta ) cos (2 \theta )$

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

$\displaystyle r^5 = 2 (2 r sin \theta r cos \theta ) ( r^2 cos^2 \theta - r^2 sin ^2 \theta )$

$\displaystyle (x^2 + y^2)^{5/2} = 4 x y ( x^2 - y^2 )$
• Dec 1st 2009, 03:45 PM
c.chav506
thanks alot mech.... you know your stuff