Find the sinusoidal signal at specific frequency

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Discussion Overview

The discussion revolves around finding the sinusoidal signal represented by a given phasor V(x) = 8 + 4j at a frequency of 50 Hz. Participants explore the conversion of the phasor into a sinusoidal form, including the calculation of amplitude and phase angle.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant calculates the amplitude as sqrt(64+16) = 8.944 and expresses uncertainty about the correctness of this result.
  • Another participant presents the sinusoidal signal as 8.944sin(100∏t + 26.56) and provides the phase angle θ calculated using tan^-1(4/8) = 26.56°.
  • A participant confirms the previous result and notes the importance of indicating the units of the arguments in the sine function, mentioning that one is in radians and the other in degrees.
  • There is a conversion of the phase angle from degrees to radians, with a participant suggesting that either representation could be acceptable.
  • Another participant mentions that the degrees version is more commonly seen in practice.

Areas of Agreement / Disagreement

Participants express differing preferences regarding the representation of the phase angle (degrees vs. radians), but there is no consensus on a single preferred method. The correctness of the initial amplitude calculation remains uncertain.

Contextual Notes

There is a lack of clarity regarding the assumptions made in the calculations, particularly in the conversion between degrees and radians, and the implications of using different units in the sine function.

DODGEVIPER13
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Homework Statement


For a phasor V(x) = 8 + 4j find the sinusoidal signal that it represents if the frequency is 50 Hz?


Homework Equations





The Attempt at a Solution


sqrt(64+16)=8.944sin(50t) so clearly this is not correct?
 
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8.944sin(100∏t+26.56)
 
where ω=2(pi)f=100(pi) and sin(ωt+θ) I found θ by tan^-1(4/8)=26.56°
 
DODGEVIPER13 said:
where ω=2(pi)f=100(pi) and sin(ωt+θ) I found θ by tan^-1(4/8)=26.56°

DODGEVIPER13 said:
8.944sin(100∏t+26.56)

Yup. That'll do it. Although strictly speaking you should indicate the units of the arguments to the sin function, since one is clearly radians and the other degrees...
 
8.944sin(100(pi)t+.463)
 
converted 26.56 to radians
 
oor would just doing 26.56°
 
Either way works. You're more likely to see the degrees version in practice.
 

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