James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

appendix D Trigonometry A31
integer multiples of , that is,
sin x − 0 whenever x − n, n an integer
Because of the identity
cos x − sinSx 1 2D
(which can be verified using Equation 12a), the graph of cosine is obtained by shifting
the graph of sine by an amount y2 to the left [see Figure 14(b)]. Note that for both
the sine and cosine functions the domain is s2`, `d and the range is the closed interval
f21, 1g. Thus, for all values of x, we have
21 < sin x < 1 21 < cos x < 1
The graphs of the remaining four trigonometric functions are shown in Figure 15 and
their domains are indicated there. Notice that tangent and cotangent have range s2`, `d,
whereas cosecant and secant have range s2`, 21g ø f1, `d. All four functions are periodic:
tangent and cotangent have period , whereas cosecant and secant have period 2.
y
y
_π
_ π 2
1
0
_1
π
2
π
3π
2
x
_π
_ π 2
0 π π 3π x
2
2
(a) y=tan x
(b) y=cot x
y
y
y=sin x
y=cos x
_ π 2
1
0
_1
π
2
π
3π
2
x
_π
_ π 2
0
_1
1
π
2
π
3π
2
x
FIGURE 15
(c) y=csc x
(d) y=sec x
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