Higher Engineering Mathematics

152 GEOMETRY AND TRIGONOMETRY

Figure 15.10

Figure 15.11

graph, then asine waveis produced as shown in

Fig. 15.10.

If all horizontal components such asOSare pro-

jected on to a graph ofyagainst anglex◦, then a

cosine waveis produced. It is easier to visualize

these projections by redrawing the circle with the

radius armORinitially in a vertical position as shown

in Fig. 15.11.

From Figures 15.10 and 15.11 it is seen that a

cosine curve is of the same form as the sine curve

but is displaced by 90◦(orπ/2 radians).

15.4 Sine and cosine curves

Graphs of sine and cosine waveforms

(i) A graph ofy=sinAis shown by the broken line

in Fig. 15.12 and is obtained by drawing up a

table of values as in Section 15.1. A similar table

may be produced fory=sin 2A.

A◦ 2 A sin 2A

000

30 60 0.866

45 90 1.0

60 120 0.866

90 180 0

120 240 −0.866

135 270 −1.0

150 300 −0.866

180 360 0

210 420 0.866

225 450 1.0

240 480 0.866

270 540 0

300 600 −0.866

315 630 −1.0

330 660 −0.866

360 720 0