Higher Engineering Mathematics, Sixth Edition

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.