236 VECTOR GEOMETRY
Now try the following exercise.
Exercise 96 Further problems on the
combination of periodic functions- Plot the graph of y=2 sinA from A= 0 ◦
to A= 360 ◦. On the same axis plot
y=4 cosA. By adding ordinates at inter-
vals ploty=2 sinA+4 cosAand obtain a
sinusoidal expression for the waveform.
[4.5 sin (A+ 63 ◦ 26 ′)] - Two alternating voltages are given byv 1 = 10
sinωtvolts andv 2 =14 sin (ωt+π/3) volts.
By plottingv 1 andv 2 on the same axes over
one cycle obtain a sinusoidal expression for
(a)v 1 +v (^2) [(b)v 1 −v 2.
(a) 20 .9 sin (ωt+ 0 .63) volts
(b) 12.5 sin (ωt− 1 .36) volts
]
In Problems 3 to 8, express the combi-
nation of periodic functions in the form
Asin (ωt±α) using phasors, either by draw-
ing or by calculation.
- 12 sinωt+5 cosωt
[13 sin (ωt+ 0 .395)]- 7 sinωt+5 sin
(
ωt+π
4)[11.11 sin (ωt+ 0 .324)]- 6 sinωt+3 sin
(
ωt−π
6)[8.73 sin (ωt− 0 .173)]6.i=25 sinωt−15 sin(
ωt+π
3)[i= 21 .79 sin (ωt− 0 .639)]7.v=8 sinωt−5 sin(
ωt−π
4)[v= 5 .695 sin (ωt+ 0 .670)]8.x=9 sin(
ωt+π
3)
−7 sin(
ωt−3 π
8)[x= 14 .38 sin (ωt+ 1 .444)]