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CHAPTER 35
35.32 Sketch the graph of r
2 = cos 2ft
The construction of the graph, Fig. 35-5, is indicated in the table of values. Note that some values of 0 yield
two values of r, and some yield none at all (when cos 20 is negative). The graph repeats from 6 = IT to
9 = 2ir. The graph is called a lemniscate.
Fig. 35-5
Fig. 35-6
35.33
Sketch the graph of r = sin 2ft
The accompanying table of values yields Fig. 35-6. The graph is called a four-leaved rose.
35.34 Sketch the graph of r = 1 - cos ft
The graph of r =/(0 - a) is the graph of r = f(6) rotated counterclockwise through a radians. Thus, a
rotation of Fig. 35-3 through IT radians gives the graph of r = 1 + cos (6 - ir) = 1 - cos ft
35.35
Sketch the graph of r = 1 - sin ft
Rotate Fig. 35-3 through 3ir/2 radians (or -IT 12 radians): r = 1+ cos (9 - 3ir/2) = 1 - sin ft
35.36
Sketch the graph of r = 1 + sin ft
Rotate Fig. 35-3 through ir/2 radians: r = 1 + cos (0 - tr/2) = 1 + sin ft
35.37
Sketch the graph of r
2 - sin 2ft
Rotate Fig. 35-5 through ir/4 radians: r
2 = cos 2(0 - ir/4) = cos (20 - -rr/2) = sin 2ft
35.38
Sketch the graph of r = 4 + 2 cos ft
See Fig. 35-7. This figure is also called a limacon (but with a "dimple" instead of a loop).
0
r
0
±1
1T/4
0
3ir/4
0
1T
±1
0
r
0
0
IT/4
1
IT/2
0
37T/4
-1
7T
0
57T/4
1
3ir/2
0
77T/4
-1
2TT
0
0
r
0
6
ir/2
4
IT
2
3ir/2
4
2ir
6