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.
The formulas to convert polar coordinates (r, θ) to rectangular coordinates (x, y) are:
\[ x = r \cos(θ) \]
\[ y = r \sin(θ) \]
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).