Trigonometric waveforms 201
908
2708
y
A8
0
21.0
1.0
y 5 sin (A 2 608)
y 5 sin A
608
608
1808
3608
Figure 22.18
1808
458
3608
A8
0
y
21.0
y 5 cos (A 1 458)
y 5 cos A
458
2708
908
Figure 22.19
Problem 7. Sketch y = 5 sin(A + 30 ◦ ) from
A = 0 ◦ to A = 360 ◦
Amplitude = 5 and period = 360
◦
/1 = 360
◦
5 sin(A + 30 ◦ ) leads 5 sin A by 30 ◦ (i.e. starts 30 ◦
earlier).
A sketch of y = 5 sin(A + 30 ◦ ) is shown in
Figure 22.20.
Problem 8. Sketch y = 7 sin(2 A − π/3) in the
range 0 ≤ A ≤ 360 ◦
Amplitude = 7 and period = 2π/2 = π radians
In general, y = sin(pt − α) lags y = sin pt by α/p,
hence 7 sin(2 A − π/3) lags 7 sin 2 A by (π/3)/2, i.e.
π/6 rad or 30
◦
A sketch of y = 7 sin(2 A − π/3) is shown in
Figure 22.21.
908
2708
A8
0
5
25
y 5 5 sin (A 1 308)
y 5 5 sin A
308
308
1808
3608
y
Figure 22.20
0
7
y
A8
3608
y 5 7 sin 2A
y 5 7 sin (2A 2␲/3)
␲/6
␲/6
2␲
␲
7
2708
1808
908
3␲/2
␲/2
Figure 22.21
Problem 9. Sketch y = 2 cos(ωt − 3π/10) over
one cycle
Amplitude = 2 and period = 2π/ω rad
2 cos(ωt − 3π/10) lags 2 cosωt by 3π/10ω seconds.
A sketch of y = 2 cos(ωt − 3π/10) is shown in
Figure 22.22.
0
y
t
␲/2␻
␲ /␻
3␲/2␻
2␲/␻
y 5 2 cos ␻t
y 52 cos(␻t 23␲/10)
22
2
3␲/10␻ rads
Figure 22.22