138 Higher Engineering Mathematics
1208908
60836083308 2 0.52 1.01.0T 0.5yR
SS 9T 9y 5 sin xAngle x 8
308 608 1208 2108 2708 33083008
270824082108180815080Figure 14.102 0.50.52 1.01.0ySR
T S^9O 9y 5 cos xAngle x 8
308 608 1208 1808 2408 3008 360845815808
3308
315828582558082258
2108
1808150812089086080Figure 14.11graph, 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 sin2A0 0 0 225 450 1.030 60 0.866 240 480 0.866
45 90 1.0 270 540 060 120 0.866 300 600 −0.86690 180 0 315 630 −1.0120 240 −0.866 330 660 −0.866
135 270 −1.0 360 720 0150 300 −0.866180 360 0210 420 0.866A graph ofy=sin2Ais shown in Fig. 14.12.