Functions and their curves 179
The simplest example of a cubic graph,y=x^3 ,is
shown in Fig. 18.3.
8 y^5 x^3
6
4
2
22
24
26
28
222112
y
x
Figure 18.3
(iv) Trigonometric Functions (see Chapter 14,
page 134)
Graphs ofy=sinθ,y=cosθandy=tanθare shown in
Fig. 18.4.
y 5 sin
y 5 cos
y 5 tan
1.0
2 1.0
2 1.0
0
2 2
3 2
2
2
1.0
0
2 2
3
(a)
(b)
(c)
0
2 2
3
y
y
y
Figure 18.4
(v) Circle(see Chapter 13, page 122)
The simplest equation of a circle is x^2 +y^2 =r^2 ,
with centre at the origin and radiusr,asshownin
Fig. 18.5.
2 r
2 r r
r
O x
x^21 y^25 r^2
y
Figure 18.5
Moregenerally, the equation of a circle, centre(a,b),
radiusr, is given by:
(x−a)^2 +(y−b)^2 =r^2
Figure 18.6 shows a circle
(x− 2 )^2 +(y− 3 )^2 = 4
024
2
3
4
5
b 53
a 52
r^5
2
(x 2 2)^21 (y 2 3)^254
y
x
Figure 18.6
(vi) Ellipse
The equation of an ellipse is
x^2
a^2
+
y^2
b^2
= 1
and the general shape is as shown in Fig. 18.7.
The lengthABis called themajor axisandCDthe
minor axis.