Higher Engineering Mathematics, Sixth Edition

142 Higher Engineering Mathematics

0

y

/2/ 3 /2 2 / t

y 5 2 cos t

y 5 2 cos(t 23 /10)

22

2

3 / 10  rads

Figure 14.24

Graphs ofsin^2 Aandcos^2 A

(i) A graph ofy=sin^2 Ais shown inFig. 14.25 using

the following table of values.

A◦ sinA (sinA)^2 =sin^2 A

0 0 0

30 0.50 0.25

60 0.866 0.75

90 1.0 1.0

120 0.866 0.75

150 0.50 0.25

180 0 0

210 −0.50 0.25

240 −0.866 0.75

270 −1.0 1.0

300 −0.866 0.75

330 −0.50 0.25

360 0 0

0

0.5

1.0

y

(^908180827083608) A 8
y 5 sin^2 A
Figure 14.25
(ii) A graph ofy=cos^2 Ais shown in Fig. 14.26
obtained by drawing up a table of values, similar
to above.
0
0.5
1.0
y
(^908180827083608) A 8
y 5 cos^2 A
Figure 14.26
(iii) y=sin^2 Aandy=cos^2 Aare both periodic func-
tions of period 180◦(orπrad) and both contain
only positive values. Thus a graph ofy=sin^22 A
has a period 180◦/2, i.e. 90◦. Similarly, a graph
ofy=4cos^23 Ahas a maximum value of 4 and a
period of 180◦/3, i.e. 60◦.
Problem 12. Sketchy=3sin^221 Ain the range
0 <A< 360 ◦.
Maximum value=3; period= 180 ◦/( 1 / 2 )= 360 ◦.
Asketchof3sin^212 Ais shown in Fig. 14.27.
0
3
y
(^908180827083608) A 8
y 5 3 sin^212 A
Figure 14.27
Problem 13. Sketchy=7cos^22 Abetween
A= 0 ◦andA= 360 ◦.
Maximum value=7; period= 180 ◦/ 2 = 90 ◦.
Asketchofy=7cos^22 Ais shown in Fig. 14.28.