Engineering Mathematics Assignment: Phasor Diagram, Trigonometry, Harmonic Synthesis, and Trigonometric Identities

Engineering Mathematics Assignment 1
ENGINEERING MATHEMATICS ASSIGNMENT
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Engineering Mathematics Assignment 2
Engineering Mathematics Assignment
Task 1
Find the sum of v1 and v2 using a phasor diagram and appropriate trigonometry
Using a phasor diagram and appropriate trigonometry, find the sum of two alternative voltages
represented by: v1 = 60 sin (500t) and v2 = sin (500t + π
5 ¿
The relative positions of v1 and v2 when t = 0 are shown in form of phasor diagrams shown in
Figure 1 below where π
5 radians=36 °. The amplitude of the equations represents the length of
the phasor diagrams. The amplitude of v1 is 60V while th amplitude of v2 is 1V.
Figure 1: Sketch of phasor diagram
Drawing this phase diagram to scale using a protractor and ruler gives the diagram shown in
Figure 2 below

Engineering Mathematics Assignment 3
Figure 2: Phasor diagram drawn to scale
The resultant voltage, VR is measured and found to be 60.8V and the angle φ is measured to be
1°. This can also be expressed in radians as follows: 1 x π
180 =0.0175 rad leading v 1
Thus by drawing and measuring, the equation for v1 + v2 becomes:
vR = v1 + v2 = 60.8 sin (500t + 0.0175) V
Task 2
I. AC circuit is given by i = 100 sin (50πt – 0.43) amps. Find amplitude, angular
frequency, periodic time, frequency and phase angle
Amplitude = 100 amps
Angular frequency, ω = 50π rad/s
Frequency, f is obtained from the angular frequency as follows
ω = 50π rad/s = 2πf; hence f = ω
2 π = 50 π
2 π =25 Hz