In polar coordinates, points are defined by a radius (r) and an angle (θ). When plotting these points, it's essential to first identify the angle before determining the position based on the radius. Angles can be expressed in both degrees and radians, which is crucial for accurate plotting.

For example, consider point A, which has coordinates (5, 60°). Here, the radius is 5, and the angle is 60 degrees, equivalent to \(\frac{\pi}{3}\) radians. To plot this point, locate the angle of 60 degrees on the polar coordinate system, then move outward along that line to a distance of 5 units, marking point A.

Next, point B is represented as (3, 90°). The radius is 3, and the angle is 90 degrees, or \(\frac{\pi}{2}\) radians. After locating the 90-degree angle, extend 3 units along that line to find point B.

Point C is given as (0, -\(\frac{5\pi}{3}\)). The radius here is 0, meaning regardless of the angle, the point will be at the origin (the pole). The negative angle indicates a clockwise measurement, but since the radius is 0, point C remains at the origin.

Finally, point D is defined by the coordinates (2, \(\frac{7\pi}{3}\)). The angle \(\frac{7\pi}{3}\) represents a full rotation plus an additional \(\frac{\pi}{3}\) radians. After completing the rotation, you would plot point D by moving 2 units outward along the corresponding line.

In summary, plotting points in polar coordinates involves determining the angle first, followed by measuring the radius from the pole. Understanding the relationship between degrees and radians, as well as how to interpret positive and negative angles, is key to accurately locating points in this coordinate system.