The equation y = x² can be converted to polar coordinates using the relationships x = r cos(θ) and y = r sin(θ). By substituting these into the equation, we derive r sin(θ) = (r cos(θ))², which simplifies to r sin(θ) = r² cos²(θ). To isolate r, one can divide both sides by r, yielding sin(θ) = r cos²(θ), while noting that r = 0 remains a valid solution. This conversion process is essential for understanding polar coordinate transformations in mathematics.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone interested in mastering coordinate transformations in mathematics.
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.stau40 said: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!