Polar to Rectangular Converter

Convert Polar to Rectangular Coordinates



What are Polar and Rectangular Coordinates?

Polar coordinates represent a point in a plane by its distance from a reference point (radius) and its angle from a reference direction. Rectangular coordinates represent a point by its horizontal (x) and vertical (y) distances from a reference point.

Conversion Formulas

The formulas to convert polar coordinates (r, θ) to rectangular coordinates (x, y) are:

\[ x = r \cos(θ) \]

\[ y = r \sin(θ) \]

Example Calculation

Consider a point with a radius of 5 units and an angle of 30 degrees:

Using the formulas:

\[ x = 5 \cos(30°) \approx 4.33 \]

\[ y = 5 \sin(30°) \approx 2.50 \]

This means the rectangular coordinates are approximately (4.33, 2.50).