Question

Find two other pairs of polar coordinates of the given polar coordinate, one with r > 0 and one with r < 0. Then plot the point.

Answer 1

To find two other pairs of polar coordinates with r > 0 and r < 0, we can change the sign of r. Use the given values of r and theta to find the polar coordinates. Plot the point by measuring the distance from the origin and rotating the angle.

Step-by-step explanation:

In polar coordinates, a point is represented by two values: the radial coordinate (r) and the angular coordinate (theta). To find two other pairs of polar coordinates with r > 0 and r < 0, we can simply change the sign of r. Let's assume the given polar coordinate is (r, theta).

1. Pair 1: (r, theta) where r > 0 will be (-r, theta). For example, if the given polar coordinate is (2, 45 degrees), then the first pair of polar coordinates will be (-2, 45 degrees).
2. Pair 2: (r, theta) where r < 0 will be (-r, theta + 180 degrees). For example, if the given polar coordinate is (2, 45 degrees), then the second pair of polar coordinates will be (-2, 225 degrees).

To plot the point, locate the origin on your graph and use the r value to measure the distance from the origin. Then, use the theta value to determine the angle of rotation from the positive x-axis.