2. The graphs in the left column are cartesian graphs of a function
r = r(t) for 0 £ t £ 2p . The graphs in the right column are the polar graphs of these functions, in some other order. Match the graphs, and then indicate with arrows how the polar graphs are traced out as t varies from 0 to 2p .

A

I

B

II

C

III

D

IV

E

V

Graph C has r(t) = 0 exactly once. Graph I is the only polar graph that goes through the origin once, so C corresponds to I.

Graph D has r(t) ³ 0 for t in [0, Pi] and r(t) £ 0 for t in [Pi, 2Pi].

Thus, in the polar graph, the curve will lie above the x-axis. So D corresponds to II.

Graph B gives the 3-leaf rose of IV as t varies from 0 to Pi and then retraces it as t goes rom Pi to 2Pi. So, B corresponds to IV.

Graph E is the graph in B, raised a bit, so it will give III

Finally, by elimination, A corresponds to V

(path alternates between a large leaf and a small leaf)