Polar to Rectangular conversion is the process of translating a point specified in polar coordinates to its equivalent position in rectangular coordinates. It involves using trigonometric functions to calculate the horizontal (x) and vertical (y) distances from the origin.
The conversion is accomplished through two simple formulas:
x= r⋅cos(θ)
y= r⋅sin(θ)
Here's an explanation of each part of the formula:
Therefore, (x) is the horizontal distance from the origin to the point, calculated by multiplying the radial distance (r) by the cosine of the angle (θ).
These formulas essentially describe how to decompose a polar coordinate (r, θ) into its rectangular components (x, y) based on trigonometric functions. The cosine function is used for the x-coordinate (horizontal position), and the sine function is used for the y-coordinate (vertical position). Together, these formulas enable the conversion between different coordinate systems, allowing us to represent points in both polar and rectangular coordinates.
Conversion:
Result:
Rectangular Coordinates (x,y) = ( , )
Conversion:
Result:
Rectangular Coordinates (x,y) = (0, -3)
Conversion:
Result:
Result: Rectangular Coordinates (x,y) = (2, )