Convert Polar to Rectangular Coordinates and Vice Versa

The rectangular coordinates (x , y) and polar coordinates (R , t) are related as follows.
y = R sin t    and    x = R cos t
R 2 = x 2 + y 2    and    tan t = y / x

polar-rectangular conversion of coordinates.

To find the polar angle t, you have to take into account the sings of x and y which gives you the quadrant.
Angle t is in the range [0 , 2?) or [0 , 360°).

Examples on Converting Polar and Rectangular Coordinates

Example 1

Convert the polar coordinates (5 , 2.01) and (0.2 , 53°) to rectangular coordinates to three decimal places.

Solution to Example 1


Example 2

Convert the rectangular coordinates (1 , 1) and (-2 ,-4) to polar coordinates to three decimal places. Express the polar angle t in degrees and radians.

Solution to Example 2

More References and Links to Polar Coordinates and Trigonometry

Convert Polar to Rectangular Coordinates Calculator .
Polar Coordinates.
Trigonometry Tutorials and Problems.