trigonometry

152 GEOMETRY AND TRIGONOMETRY
Figure 15.10
Figure 15.11
graph, then a sine wave is produced as shown in
Fig. 15.10.
If all horizontal components such as OS are projected
on to a graph of y against angle x ◦ , then a
cosine wave is produced. It is easier to visualize
these projections by redrawing the circle with the
radius arm OR initially 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 ◦ (or π/2 radians).
15.4 Sine and cosine curves
Graphs of sine and cosine waveforms
(i) A graph of y = sin A is 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 for y = sin 2A.
A ◦ 2A sin 2A
0 0 0
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