Final answer:
The process of converting between rectangular coordinates and polar coordinates involves trigonometric functions to relate the Cartesian coordinates (x, y) to the polar coordinates (r, θ), dependent on whether the conversion goes from polar to rectangular or vice versa.
Step-by-step explanation:
Converting between polar coordinates and rectangular coordinates involves the use of trigonometric relationships and algebraic transformations. In the polar coordinate system, a point is defined by the distance from the origin (r) and the angle (θ) with respect to the positive x-axis.
To convert from polar to rectangular coordinates (x, y), we use the equations x = r × cos(θ) and y = r × sin(θ).
Conversely, to convert from rectangular to polar coordinates, we use r = √(x^2 + y^2) and θ = atan2(y, x), where atan2(y, x) is the two-argument arctan function that takes into account the sign of both arguments to determine the correct quadrant of θ.