How to Convert from Polar to Cartesian Coordinates
Converting from Polar to Cartesian Coordinates
Polar coordinates can be converted to Cartesian coordinates using the following formulas:
In these formulas:

x is the xcoordinate of the point in Cartesian coordinates.

y is the ycoordinate of the point in Cartesian coordinates.

r is the radial coordinate of the point in polar coordinates.

θ is the angular coordinate of the point in polar coordinates.
The graph below shows what we mean by the same point defined in polar coordinates (r, θ) and Cartesian coordinates (x, y):
How to Convert from Polar to Cartesian Coordinates
Converting from the polar to the Cartesian coordinates of a point is easy.
Question
What is a point described by the polar coordinates (8, 30°) in Cartesian coordinates?
StepbyStep:
Find the XCoordinate
2
Find r and θ from the polar coordinates given in the question.
In our example, the polar coordinates of the point is (8, 30°). They are represented in the formula by (r, θ).
(r, θ) = (8, 30°) ∴ r = 8, θ = 30°
3
Substitute r and θ into the formula.
xcoordinate = 8 cos (30°)
xcoordinate = 8 × 0.87
xcoordinate = 6.9
The xcoordinate is 6.9
Find the YCoordinate
4
5
Substitute r and θ into the formula.
ycoordinate = 8 sin (30°)
ycoordinate = 8 × 0.5
ycoordinate = 4
The ycoordinate is 4
6
Write down the Cartesian coordinates as a pair of numbers in brackets, separated by a comma.
The xcoordinate (6.9) found in Step 3 goes on the left.
The ycoordinate (4) found in Step 5 goes on the right.
Answer:
The polar coordinates (8, 30°) become (6.9, 4) when converted to Cartesian coordinates.