Trigonometric waveforms 201
908 2708y(^0) A 8
2 1.0
1.0 y^5 sin (A^2608 )
y 5 sin A
608
608
1808 3608
Figure 22.18
1808
458
(^03608) A 8
y
2 1.0
y 5 cos (A 1458 )
y 5 cos A
458
908 2708
Figure 22.19
Problem 7. Sketchy=5sin(A+ 30 ◦)from
A= 0 ◦toA= 360 ◦
Amplitude= 5 andperiod= 360 ◦/ 1 = 360 ◦
5sin(A+ 30 ◦)leads5sinA by 30◦ (i.e. starts 30◦
earlier).
Asketchofy=5sin(A+ 30 ◦) is shown in
Figure 22.20.
Problem 8. Sketchy=7sin( 2 A−π/ 3 )in the
range 0≤A≤ 360 ◦
Amplitude= 7 andperiod= 2 π/ 2 =πradians
In general,y=sin(pt−α)lagsy=sinptbyα/p,
hence 7sin( 2 A−π/ 3 )lags 7sin2Aby(π/ 3 )/2, i.e.
π/6 rad or 30◦
Asketchofy=7sin( 2 A−π/ 3 ) is shown in
Figure 22.21.
(^09082708) A 8
5
25
y 5 5 sin (A 1308 )
y 5 5 sin A
308
308
(^18083608)
y
Figure 22.20
0
7
y
(^3608) A 8
y 5 7 sin 2A
y 5 7 sin (2A 2 /3)
/6
/6
2
7
908 1808 2708
/ 2 3 / 2
Figure 22.21
Problem 9. Sketchy=2cos(ωt− 3 π/ 10 )over
one cycle
Amplitude= 2 andperiod= 2 π/ωrad
2cos(ωt− 3 π/ 10 )lags2cosωtby 3π/ 10 ωseconds.
Asketchofy=2cos(ωt− 3 π/ 10 ) is shown in
Figure 22.22.
0
y
/2/ 3 /2 2 / t
y 5 2 cos t
y 5 2 cos(t 23 /10)
22
2
3 / 10 rads
Figure 22.22