Higher Engineering Mathematics

FUNCTIONS AND THEIR CURVES 195

C

0 π

2

π3π

2

2π θ

1

3

y = cos θ + 2

y = cos θ

(b)

Figure 19.14

π

2

π 3 π

2

0 2 π x

− 1

1

y

π

3

y = sin x− π 3

y = sinx

(a)

π

(^3) ( )
π
2
π 3 π
2
(^02) πx
− 1
1
y
π
4
y = sin x+ π 4
y = sinx
π
4
(b)
( )
Figure 19.15
Figure 19.16
For example, if f(x)=(x−1)^2 , and a=
1
2
, then
f(ax)=
(x
2
− 1
) 2
.
Both of these curves are shown in Fig. 19.17(a).
Similarly,y=cosx andy=cos 2x are shown in
Fig. 19.17(b).