Converting Cartesian to Polar Coordinates: How Do We Get r and Theta?

[GloryUs]

Homework Statement

Write equation in polar form. y=3x+4

Homework Equations

x^2 + y^2 = r^2
x = rcos(theta)
y = rsin(theta)
tan(theta) = y/x

The Attempt at a Solution

Square both sides...
y^2 = 9x^2 + 24x + 16

r^2 - x^2 = 9x^2 +24x +16

r^2 = 10x^2 + 24x + 16

And that's where I got stuck...

 

[learningphysics]

Don't do it like that. Substitute the polar form of x and y into your equation... and you'll be done.

 

[HallsofIvy]

Replace EVERY x with r cos(\thet and EVERY y with r sin(\theta)

 

[JonF]

What is your goal in converting from Cartesian to polar coordinates? You want to get a function that is:
r = a bunch of theta junk

So how do we turn y=3x+4 into an equation of nothing but r’s and theta’s? We use the two substations you have, then we get r all by it self on one side.