294
Fig. 35-10
Fig. 35-11
35.44 Sketch the graph of r = sin (0/2).
I See Fig. 35-11. From 0 = 0 to 0 = 277, we obtain a "cardioid", and then, from 0 = 2ir to 0 = 477,
the reflection of the first "cardioid" in the y-axis.
35.45 Sketch the graph of r = cos
2 (6/2).
r = cos
2 (0/2) = (1 + cos0)/2. Hence, the graph is a contraction toward the pole by a factor of 3, of
Fig. 35-3.
35.46 Sketch the graph of r = tan ft
The behavior of tan 6 is shown in the table of values. Recall that tan0-»+°° as 6->(ir/2)~, and
tan0-»-77 as 0-»(77/2)
+ . See Fig. 35-12.
Fig. 35-12
Fig. 35-13
35.47 Sketch the graph of r = sin 3ft
It is convenient to use increments in 0 of 77/6 to construct Fig. 35-13. Note that the graph repeats itself after
0 = 77. The result is a three-leaved rose.
0
/•
0
0
7T/6
1
77/3
0
77/2
-1
277/3
0
577/6
1
77
0
0
r
0
0
77/2
V2/2
77
1
37T/2
V2/2
277
0
577/2
-V2/2
37T
-1
7ir/2
-V2/2
47T
0
CHAPTER 35
e
r
0
0
7T/4-»7r/2<-37r/4
1— » +oo ; — oo <
1
77
0
57j74-»3w/2«-77T/4
1— » +00, — oo<
1
277
0
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