Enter the radius and angle to convert polar coordinates to Cartesian coordinates or vice versa.
Polar Coordinates to Cartesian Conversion
The conversion between polar coordinates and Cartesian coordinates is a fundamental concept in mathematics and physics. Polar coordinates are represented as (r, θ), where ‘r’ is the radius or distance from the origin, and ‘θ’ is the angle in degrees from the positive x-axis. Cartesian coordinates, on the other hand, are represented as (x, y), where ‘x’ and ‘y’ are the horizontal and vertical distances from the origin, respectively.
To convert from polar to Cartesian coordinates, you can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
These formulas allow you to determine the Cartesian coordinates (x, y) from the polar coordinates (r, θ). Conversely, to convert Cartesian coordinates to polar coordinates, you can use the formulas:
r = √(x² + y²)
θ = atan2(y, x)
Here, ‘√’ denotes the square root, and ‘atan2’ is the two-argument arctangent function, which returns the angle θ in degrees.
Understanding Polar and Cartesian Coordinates
Polar coordinates are particularly useful in scenarios where relationships are more naturally expressed in terms of angles and