How do I convert the equation y = x^(2) to polar coordinates?

[stau40]

Homework Statement

Convert to an equation in polar coordinates y = x^(2)

Homework Equations

x = r cos (theta) , y = r sin (theta) , tan (theta) = y/x

The Attempt at a Solution

Here is my work so far: y=x^(2) so r sin (theta) = (r cos (theta))^2 and r sin (theta) = r^(2) cos^(2) theta. I'm not sure how to move the r's to one side of the equation though. Can I apply tan (theta) = y/x or ? Thanks in advance!

 

[Mark44]

Homework Statement

Convert to an equation in polar coordinates y = x^(2)

Homework Equations

x = r cos (theta) , y = r sin (theta) , tan (theta) = y/x

The Attempt at a Solution

Here is my work so far: y=x^(2) so r sin (theta) = (r cos (theta))^2 and r sin (theta) = r^(2) cos^(2) theta. I'm not sure how to move the r's to one side of the equation though. Can I apply tan (theta) = y/x or ? Thanks in advance!

You can divide both sides of your equation by r to get sin(theta) = rcos^2(theta). It's not always legitimate to do this, as you might be losing solutions for r = 0. In this case, r = 0 is still a solution.