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.
$r= \sqrt{x^2+y^2}$
and θ is given by the arctan of the ratio of y to x.
$\theta=\tan^{-1} \frac{y}{x}$
Example:
To convert rectangular coordinate (3, 4) to polar coordinate
$r= \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} =5 \\ \theta=\tan^{-1}( \frac{4}{3}) =53.13^o$
Therefore, rectangular coordinate (3, 4) = polar coordinate (5, 53.13°)