138 Higher Engineering Mathematics
1208
908
608
3608
3308 2 0.5
2 1.0
1.0
T 0.5
y
R
S
S 9
T 9
y 5 sin x
Angle x 8
308 608 1208 2108 2708 3308
3008
2708
2408
2108
1808
1508
0
Figure 14.10
2 0.5
0.5
2 1.0
1.0
y
S
R
T S^9
O 9
y 5 cos x
Angle x 8
308 608 1208 1808 2408 3008 3608
458
15808
3308
3158
2858
2558
08
2258
2108
1808
1508
1208
908
608
0
Figure 14.11
graph, then asine waveis produced as shown in
Fig. 14.10.
If all horizontal components such asOSare projected
on to a graph ofyagainst anglex◦,thenacosine wave
is produced. It is easier to visualize these projections by
redrawing the circle with the radius armORinitially in
a vertical position as shown in Fig. 14.11.
From Figs. 14.10 and 14.11 it is seen that a cosine
curve is of the same form as the sine curve but is
displaced by 90◦(orπ/2radians).
14.4 Sine and cosine curves
Graphs of sine and cosine waveforms
(i) A graph ofy=sinAis shown by the broken line
in Fig. 14.12 and is obtained by drawing upa table
of values as in Section 14.1. A similar table may
be produced fory=sin2A.
A◦ 2 A sin2A A◦ 2 A sin2A
0 0 0 225 450 1.0
30 60 0.866 240 480 0.866
45 90 1.0 270 540 0
60 120 0.866 300 600 −0.866
90 180 0 315 630 −1.0
120 240 −0.866 330 660 −0.866
135 270 −1.0 360 720 0
150 300 −0.866
180 360 0
210 420 0.866
A graph ofy=sin2Ais shown in Fig. 14.12.