Question

Plot the point that has the given polar coordinates. Then give two other polar coordinate representations of the point, one with r<0 and the other with r>0 . (3,1)

Answer 1

To plot the point with polar coordinates (3,1), start from the origin and move 3 units in the direction of the angle θ and 1 unit perpendicular to θ. The point can also be represented as (-3,-1) and (3,π+1) with different values of r.

Step-by-step explanation:

Polar coordinates consist of a distance from the origin (r) and an angle (θ) that the line from the origin to the point makes with the positive x-axis. The given polar coordinates are (3,1). To plot this point, starting from the origin, move 3 units in the direction of the angle θ (which is measured counterclockwise from the positive x-axis) and 1 unit in the direction perpendicular to the angle θ. The point (3,1) can also be represented as (-3,-1) with r < 0 and (3,π+1) with r > 0.