How do you convert polar coordinates to Cartesian coordinates? And vise versa.
Since this is not my area of expertise, I searched Google under the key words "polar Cartesian coordinates" to get this:
http://www.google.com/search?client=safari&rls=en&q=polar+Cartesian+coordinates&ie=UTF-8&oe=UTF-8
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
To convert polar coordinates to Cartesian coordinates, you can use the following formulas:
Given a polar coordinate (r, θ), where r represents the distance from the origin and θ represents the angle from the positive x-axis:
- The x-coordinate in Cartesian coordinates is given by: x = r * cos(θ)
- The y-coordinate in Cartesian coordinates is given by: y = r * sin(θ)
To convert Cartesian coordinates to polar coordinates, you can use the following formulas:
Given a Cartesian coordinate (x, y):
- The distance from the origin (r) in polar coordinates is calculated using the Pythagorean theorem: r = sqrt(x^2 + y^2)
- The angle (θ) in polar coordinates can be found using trigonometric functions:
- If x > 0 and y ≥ 0: θ = atan(y/x)
- If x < 0: θ = atan(y/x) + π
- If x > 0 and y < 0: θ = atan(y/x) + 2π
- If x = 0 and y > 0: θ = π/2
- If x = 0 and y < 0: θ = 3π/2
- If x = 0 and y = 0: Undefined angle
These formulas allow you to convert between polar and Cartesian coordinates using the given values of radius and angle, or x and y coordinates, respectively.