Which coordinate system combines both angular and linear measurements?

The polar coordinate system is designed to represent points in a two-dimensional space using a combination of angular and linear measurements. In this system, a point is described by the distance from a reference point, typically the origin, and the angle from a reference direction, usually the positive x-axis.

This combination allows for a more versatile representation of points when dealing with circular or rotational movement, as it captures both how far out from the origin a point is (the radial coordinate) and the direction from the origin (the angular coordinate). This is particularly useful in fields such as navigation, engineering, and physics, where angles and distances are key components.

In contrast, the other coordinate systems listed, such as rectangular, spherical, and cylindrical, primarily focus on either linear measurements or angular measurements alone or in specific contexts. The rectangular system uses linear measurements along perpendicular axes, the spherical system utilizes both angles and a radius but is specifically designed for three-dimensional spaces, and the cylindrical system combines linear heights with a circle but does not inherently mix linear and angular in the same straightforward manner as polar coordinates do.