# Polar to cartesian

• May 28th 2008, 10:02 AM
bcvw85
Polar to cartesian
Hi have a question which requires changing polar coordiantes to cartesian for the equation r=exp(titah)

using
r = (sqrt(x^2+y^2)
titah = arctan(y/x)
r = x/cos(titah) = y/sin(titah)

i get this equation

sqrt(x^2+y^2) = exp(arctan(x/y)
ln(sqrt(x^2+y^2)=arctan(x/y)

any help on how to separate the variables? to form an equation y=f(x)
• May 28th 2008, 10:14 AM
Chris L T521
Quote:

Originally Posted by bcvw85
Hi have a question which requires changing polar coordiantes to cartesian for the equation r=exp(titah)

using
r = (sqrt(x^2+y^2)
titah = arctan(y/x)
r = x/cos(titah) = y/sin(titah)

i get this equation

sqrt(x^2+y^2) = exp(arctan(x/y)
ln(sqrt(x^2+y^2)=arctan(x/y)

any help on how to separate the variables? to form an equation y=f(x)

$r=e^\theta$

$\therefore x^2+y^2=e^{2\arctan\left(\frac{y}{x}\right)}$

$\ln(x^2+y^2)=2\arctan\left(\frac{y}{x}\right)$

I don't think we can get y by itself...(Wondering)
• May 28th 2008, 10:17 AM
bcvw85
Yeah i thought so...was running around in circles in those equations for a while!

I'm actually trying to find a parameterization(x(t),y(t)) for r=exp(titah).

So if i can't isolate the y in the equation, how do i perform this parameterization?