When we know a point in Polar Coordinates (r, θ), and we want it in Cartesian Coordinates (x,y) we solve a right triangle with a known long side and angle: Example: What is (13, 22.6°) in Cartesian Coordinates? Use the Cosine Function for x:Īnswer: the point (13, 22.6°) is almost exactly (12, 5) in Cartesian Coordinates. Note: Calculators may give the wrong value of tan-1 () when x or y are negative. Summary: to convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):

Inverse Tangent takes a ratio (like '5/12') and gives us an angle.

Tangent takes an angle and gives us a ratio,.

Use the Tangent Function to find the angle: tan( θ ) = 5 / 12 θ = tan-1 ( 5 / 12 ) = 22.6° (to one decimal)Īnswer: the point (12,5) is (13, 22.6°) in Polar Coordinates. Example: What is (12,5) in Polar Coordinates? When we know a point in Cartesian Coordinates (x,y) and we want it in Polar Coordinates (r, θ) we solve a right triangle with two known sides. To convert from one to the other we will use this triangle: To Convert from Cartesian to Polar Using Polar Coordinates we mark a point by how far away, and what angle it is: Using Cartesian Coordinates we mark a point by how far along and how far up it is:

To pinpoint where we are on a map or graph there are two main systems: Cartesian Coordinates

Python polar to cartesian with math