The polar coordinate system is a two-dimensional mathematical coordinate system that serves as an alternative to the familiar Cartesian coordinate system. In the polar coordinate system, points are referenced from a central origin identical to that of the Cartesian system, point (0,0). Polar points are generally described by the variables "r," representing a radial distance from the origin, and "θ," which represents the angle from an arbitrary axis. Polar equations can be found from a Cartesian equation expressed in terms of "x" and "y."
Instructions
-
-
1
Solve your Cartesian coordinate system equation for "y." For example, solving the equation 3x = y + 5 for "y" gives the equation y = 3x - 5.
-
2
Set "y" equal to "(r)sin(θ)." Following the example equation, y = 3x - 5, this is your new equation:
(r)sin(θ) = 3x - 5.
-
-
3
Replace any "x" in the equation with "(r)cos(θ)." Replacing "x" in our example equation yields this equation:
(r)sin(θ) = (3r)cos(θ) - 5.
-
4
Solve the equation for "r" in terms of "θ." Solving our example equation yields this equation:
r = 5 / [3cos(θ) - sin(θ)].