Question

The phasor technique makes it pretty easy to combine several sinusoidal functions into a single sinusoidal expression without using trigonometric identities. However, you cannot use the phasor technique in all cases. Select the expressions below for which the phasor technique cannot be used to combine the sinusoids into a single expression. Check all that apply. View Available Hint(s) Check all that apply. −100sin(10,000t+90∘)+40sin(10,100t−80∘)+80cos(10,000t) 100cos(500t+40∘)+50sin(500t−120∘)−120cos(500t+60∘) 25cos(50t+160∘)+15cos(50t+70∘) 45sin(2500t−50∘)+20cos(1500t+20∘) 75cos(8t+40∘)+75sin(8t+10∘)−75cos(8t+160∘)

Answer 1

Answer: The applicable answers are as follows:

a) 100 cos (500t + 40º) + 50 sin (500t - 120º) -120 cos (500t + 60º)

b) 25 cos (50t + 60º) + 15 cos (50t + 70º)

c) 75 cos (8t + 40º) +75 sin (8t + 10º) -75 cos (8t +160º)

Step-by-step explanation:

A phasor, is a tool created in order to be able to represent a "snapshot"of a signal, of a fixed frequency, amplitude and phase, drawing it like a vector that is rotating continuously at a given frequency.

The actual frequency is not relevant for the drawing, that simply shows a vector, which module is the instantaneous amplitude of the signal, and the angle with the horizontal (taking a pair of perpendicular axes in order to have an amplitude and phase reference), the instantaneous phase of the signal.

If we have several sinusoids of different amlipitudes and phases, but of the same frequency, we can get the combination of these, as a single sinusoid with a given amplitude and phase, just adding the different sinusoids like they were vectors.

But if the frequencies are different, as the relative phases are changing all the time, it makes no sense to try to use this technique.

In those cases, it must be used the superposition principle only.