POLAR COORDINATES
Fig. 35-7
35.39
Sketch the graph of r = 2 + 4 cos 0.
Scale up Fig. 35-4 by the factor 2.
35.40
Sketch the graph of r = 4 - 2 sin ft
Rotate Fig. 35-7 through 3ir/2 (or -7r/2) radians: r = 4 + 2 cos (9 - 3u-/2) = 4 - 2 sin ft
35.41
Sketch the graph of r = 2a sin ft
See Problem 35.13. A geometrical construction is shown in Fig. 35-8, for the case a >0.
Fig. 35-8
Fig. 35-9
35.42
Sketch the graph of r
2 = sin ft
35.43
Sketch the graph of r = 2 f cos 2ft
r is never negative. The graph, Fig. 35-10, is symmetric with respect to the pole, since cos 2(0 + ir) =
cos 2ft
e
r
0
3
IT/4
2
IT/2
1
3W4
2
it
3
57T/4
2
3ir/2
1
77T/4
2
27T
3
293
e
r
0
0
IT/2
±1
17
0
2n
0
As shown in Fig. 35-9, the curve is a lemniscate.