Polar to Rectangular Calculator
Rectangular coordinates, or cartesian coordinates, come in the form (x, y), points are identified by their distances from the x and y axes. Polar coordinates, on the other hand, come in the form (r, θ), points are identified by their angle on the unit circle and their distance from the origin.
What is Polar to Rectangular Calculator?
'Polar to Rectangular Calculator' is an online tool that helps to convert polar to rectangular coordinates. Online Polar to Rectangular Calculator helps you to convert polar to rectangular coordinates in a few seconds.
Polar to Rectangular Calculator
How to Use Polar to Rectangular Calculator?
Please follow the below steps to convert polar to rectangular coordinates:
- Step 1: Enter the polar coordinates(r, θ) in the given input boxes.
- Step 2: Click on the "Convert" button to convert polar to rectangular coordinates.
- Step 3: Click on the "Reset" button to clear the fields and enter the different values.
How to Find Polar to Rectangular Calculator?
Polar coordinates are expressed as (r, θ) while rectangular coordinates are expressed as (x,y)
Converting polar to rectangular coordinates means expressing the polar coordinates in the form of rectangular coordinates.
The formula's for converting polar coordinates to rectangular coordinates:
x = rcosθ, y = rsinθ
Where (r, θ) are polar coordinates and (x, y) are rectangular coordinates
Solved Examples on Polar to Rectangular Calculator
Example 1:
Convert polar coordinates (5, 45°) into rectangular coordinates.
Solution:
Given: r = 5, θ = 45°
To convert polar to rectangular coordinates,
x = rcosθ
= 5cos45°
= 5 / √2
x = 3.536
y = rsinθ
= 5 sin45°
= 5 / √2
y = 3.536
Therefore, rectangular coordinates (x, y) = (3.536, 3.536)
Example 2:
Convert polar coordinates (7, 30°) into rectangular coordinates.
Solution:
Given: r = 7, θ = 30°
To convert polar to rectangular coordinates,
x = rcosθ
= 7cos30°
= 7(√3/2)
x = 6.06
y = rsinθ
= 7 sin30°
= 7 / 2
y = 3.5
Therefore, rectangular coordinates (x, y) = (6.06, 3.5)
Example 3:
Convert polar coordinates (4, 60°) into rectangular coordinates.
Solution:
Given: r = 4, θ = 60°
To convert polar to rectangular coordinates,
x = rcosθ
= 4cos60°
= 4 / 2
x = 2
y = rsinθ
= 4 sin30°
= 4(√3/2)
y = 3.465
Therefore, rectangular coordinates (x, y) = (2, 3.465)
Similarly, you can use the calculator to convert polar to rectangular coordinates for the following:
- Convert polar coordinates (11, 60) into rectangular coordinates
- Convert polar coordinates (7, 30) into rectangular coordinates