CHAP. 27]
185
GRAPHS OF THE TRIGONOMETRIC FUNCTIONS
Table 27.2 x
y ¼ sin x
y ¼ cot x
y ¼ sec x
y ¼ csc x
0
1.00
0
61
1.00
61
0.50
0.87
0.58
1.73
1.15
2.00
p=4
0.71
0.71
1.00
1.00
1.41
1.41
p=3
0.87
0.50
1.73
0.58
2.00
1.15
p=2
1.00
0
61
0
61
1.00
2p=3
0.87
0:50
1:73
0:58
2:00
1.15
3p=4
0.71
0:71
1:00
1:00
1:41
1.41
5p=6
0.50
0:87
0:58
1:73
1:15
2.00
p
1:00
0
þ1
1:00
þ1
7p=6
0:50
0:87
0.58
1.73
1:15
2:00
5p=4
0:71
0:71
1.00
1.00
1:41
1:41
4p=3
0:87
0:50
1.73
0.58
2:00
1:15
3p=2
1:00
0
61
0
61
1:00
0
5p=3
0:87
0.50
1:73
0:58
2.00
1:15
7p=4
0:71
0.71
1:00
1:00
1.41
1:41
11p=6
0:50
0.87
0:58
1:73
1.15
2:00
61
1.00
61
2p
Note 2.
y ¼ tan x
p=6
0
Note 1.
y ¼ cos x
0
1.00
0
Since sin 12p þ x ¼ cos x; the graph of y ¼ cos x may be obtained most easily by shifting the graph of y ¼ sinx a distance 12 p to the left. See Fig. 27-5.
1
Fig. 27-5
Since csc 2p þ x ¼ sec x; the graph of y ¼ csc x may be obtained by shifting the graph of y ¼ sec x a distant 12 p to the right. Notice, too, the relationship between the graphs for tan x and cot x. See Figs. 27-6 through 27-9.
Fig. 27-6
Fig. 27-7