How to converting rectangular equations into polar equations
Three formulas for converting between rectangular and polar equations
To convert rectangular equations to polar equations, we’ll use the following conversion formulas.
???x=r\cos{\theta}???
???y=r\sin{\theta}???
???r^2=x^2+y^2???
How to convert an equation from rectangular coordinates to polar coordinates
Take the course
Want to learn more about Calculus 2? I have a step-by-step course for that. :)
An example of converting a rectangular equation into polar coordinates
Example
Convert the rectangular equation to a polar equation.
???x^2-3x+y^2+2y=0???
Use ???r^2=x^2+y^2???.
???x^2+y^2-3x+2y=0???
???r^2-3x+2y=0???
Use ???x=r\cos{\theta}??? and ???y=r\sin{\theta}???.
???r^2-3r\cos{\theta}+2r\sin{\theta}=0???
???r^2=3r\cos{\theta}-2r\sin{\theta}???
???r=3\cos{\theta}-2\sin{\theta}???
Once we’ve eliminated all ???x??? and ???y??? variables, and replaced them with ???r??? and ???\theta??? variables, we’re done with the conversion.