When getting phase angle difference, do amplitudes have to be positive

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Discussion Overview

The discussion revolves around the determination of phase angle differences between two sinusoidal functions, specifically examining whether amplitudes must be positive and how phase angles are defined in this context. The scope includes mathematical reasoning and conceptual clarification related to trigonometric functions.

Discussion Character

  • Mathematical reasoning, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents two sinusoidal functions and questions whether the phase angle difference is 15° and if the amplitudes must be positive.
  • Another participant notes a mathematical identity involving negative sine functions, suggesting a relationship between phase angles.
  • A further reply discusses the implications of the identity and provides an alternative phase angle representation, leading to a different calculated phase angle difference of 165°.
  • Another participant emphasizes that the phase difference should be determined by comparing corresponding points on the graphs of the functions, arguing that both phase angles should be expressed with the same sign, asserting that 225° is the correct value for the phase difference.

Areas of Agreement / Disagreement

Participants express differing views on the correct phase angle difference and whether amplitudes must be positive. There is no consensus on the correct approach to determining the phase angle difference.

Contextual Notes

The discussion includes various mathematical identities and interpretations of phase angles, which may depend on the definitions used and the specific context of the sinusoidal functions.

Vishera
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$$f(x)=32sin(x+60°)\quad and\quad g(x)=-1.5sin(x+45°)$$

Would the phase angle difference here be 15° or is that incorrect? I think the amplitudes don't have to be the same but I'm not sure if they at least have to be both positive.
 
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-sin(a) = sin(a+π). See what happens.
 
n = 180 and a<90, for -sin(a) = sin(a+n)
 
$$-1.5sin(x+45°)\\ =1.5sin(x+225°)$$

Here the phase angle difference is 165°. So which would be more correct? The phase angle difference is simply defined as the difference between the two phase angles in two sinusoids, right? So are they both right?
 
When you look at the graphs, the phase difference is the difference between corresponding points (e.g. max) on the the two curves. Therefore they both need to expressed with the same sign. In this case 225° is the correct value for phase difference.
 

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