Question

Convert the rectangular equation to polar form.

Answer 1

To convert from rectangular coordinate (x, y) to polar coordinate (r, θ).
r is given by the square root of the sum of the squares of the rectangular coordinate.

`r= √(x^2+y^2)`
and θ is given by the arctan of the ratio of y to x.

`\theta=\tan^(-1) (y)/(x)`
Example:
To convert rectangular coordinate (3, 4) to polar coordinate

`r= √(3^2+4^2) = √(9+16) = √(25) =5 \\ \theta=\tan^(-1)( (4)/(3)) =53.13^o`
Therefore, rectangular coordinate (3, 4) = polar coordinate (5, 53.13°)