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 radians and degrees, which is crucial for accurate plotting.

For example, consider point A, which has coordinates (5, 60°). To plot this, convert 60 degrees to radians, which is \frac{\pi}{3} . Start by locating the angle of \frac{\pi}{3} on the polar coordinate system. From this angle, move outward along the line to a distance of 5 units to find point A.

Next, point B is represented as (3, 90°). The angle of 90 degrees corresponds to \frac{\pi}{2} radians. After locating this angle, extend 3 units along the line to reach point B.

Point C is given as (0, - \frac{5\pi}{3} ). The negative angle indicates a clockwise measurement. First, locate - \frac{5\pi}{3} , which brings you back to the same line as point A. However, since the radius is 0, point C remains at the origin, or the pole.

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} . After completing the rotation, move 2 units outward to find point D.

By understanding how to convert between degrees and radians and how to interpret the radius and angle, you can effectively plot points in polar coordinates. Practice with various points to strengthen your skills in this coordinate system.