About Polar Coordinates Calculator (Formula)
A Polar Coordinates Calculator is a tool used to convert between polar coordinates (r, θ) and Cartesian coordinates (x, y). Polar coordinates are a different way of representing points in a plane compared to the more familiar Cartesian coordinates. The formulae for converting between polar and Cartesian coordinates are as follows:
Converting from Polar to Cartesian Coordinates:
- x = r * cos(θ)
- y = r * sin(θ)
Converting from Cartesian to Polar Coordinates:
- r = √(x² + y²)
- θ = atan2(y, x)
Where:
- (x, y): Cartesian coordinates representing the point’s position on the plane.
- (r, θ): Polar coordinates representing the point’s distance from the origin and the angle formed with the positive x-axis.
For example, given a point with polar coordinates (r = 3, θ = π/4), the Cartesian coordinates can be calculated as:
- x = 3 * cos(π/4) ≈ 2.121
- y = 3 * sin(π/4) ≈ 2.121
Conversely, for a point with Cartesian coordinates (x = 5, y = -5), the polar coordinates can be calculated as:
- r = √(5² + (-5)²) ≈ 7.071
- θ = atan2(-5, 5) ≈ -0.785 (in radians, or about -45 degrees)
The Polar Coordinates Calculator is valuable in various fields, including mathematics, physics, and engineering, especially when dealing with problems involving circular or radial symmetry. It’s a convenient way to represent points in scenarios where angles and distances from a central point are significant.