trigonometry

154 GEOMETRY AND TRIGONOMETRY
Amplitude
Amplitude is the name given to the maximum or
peak value of a sine wave. Each of the graphs
shown in Figs. 15.12 to 15.15 has an amplitude of
+1 (i.e. they oscillate between +1 and −1). However,
if y = 4 sin A, each of the values in the table
is multiplied by 4 and the maximum value, and
thus amplitude, is 4. Similarly, if y = 5 cos 2A, the
amplitude is 5 and the period is 360 ◦ /2, i.e. 180 ◦ .
Problem 7. Sketch y = 4 cos 2x from x = 0 ◦ to
x = 360 ◦ .
Amplitude = 4; period = 360 ◦ /2 = 180 ◦ .
A sketch of y = 4 cos 2x is shown in Fig. 15.18.
Problem 5. Sketch y = sin 3A between A = 0 ◦
and A = 360 ◦ .
Amplitude = 1; period = 360 ◦ /3 = 120 ◦ .
A sketch of y = sin 3A is shown in Fig. 15.16.
Figure 15.18
Problem 8.
cycle.
Sketch y = 2 sin 3 A over one
5
Figure 15.16
Amplitude = 2; period = 360◦
3
5
= 360◦ × 5
3
= 600 ◦ .
A sketch of y = 2 sin 3 A is shown in Fig. 15.19.
5
Problem 6. Sketch y = 3 sin 2A from A = 0to
A = 2π radians.
Amplitude = 3, period = 2π/2 = π rads (or 180 ◦ ).
A sketch of y = 3 sin 2A is shown in Fig. 15.17.
Figure 15.19
Lagging and leading angles
Figure 15.17
(i) A sine or cosine curve may not always start
at 0 ◦ . To show this a periodic function is represented
by y = sin(A ± α) ory = cos(A ± α)