How do you describe transformations in a sinusoid?

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Discussion Overview

The discussion centers on how to describe transformations in sinusoidal functions, specifically focusing on the concept of amplitude and its properties. Participants explore the definition of amplitude in the context of sinusoidal equations and clarify misconceptions regarding negative values.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions how to describe transformations when the amplitude appears to change from 1 to -2.
  • Another participant asserts that amplitude is defined as a positive real number, emphasizing that it is represented by the absolute value of the coefficient in the sinusoidal function.
  • A participant expresses confusion regarding the notion of negative amplitude, citing a specific function and suggesting that its amplitude might be -2.
  • Further clarification is provided that amplitude is the distance from the equilibrium to the extrema, reinforcing that it is a non-negative value.
  • Participants agree that the amplitude of the function in question is calculated as the absolute value of -2, resulting in an amplitude of 2.

Areas of Agreement / Disagreement

There is a general agreement among participants that amplitude is a non-negative value, but initial confusion regarding the concept of negative amplitude indicates some disagreement or misunderstanding that needed clarification.

Contextual Notes

Participants rely on the definition of amplitude as the absolute value of the coefficient in sinusoidal functions, which may depend on the context of the discussion and the specific forms of the functions being analyzed.

mathdrama
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How exactly do you describe transformations? For instance, if the amplitude has gone from 1 to -2, how would you word that?
 
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Re: wording transformations

If you are referring to the amplitude of a sinusoid, the amplitude is a positive real number. For example, the sinusoid:

$$f(x)=A\sin(Bx+C)+D$$ where $A\ne0$

has an amplitude of $|A|$.

The amplitude is half the difference between the maximum and minimum of the function. So, if the amplitude changes, then so do the extrema.
 
The amplitude is never negative? I must be doing this wrong.

I had assumed the amplitude of this function: [math] - 2 cos 3(\theta + 90°) + 1 [/math] must be -2
 
mathdrama said:
The amplitude is never negative? I must be doing this wrong.

I had assumed the amplitude of this function: [math] - 2 cos 3(\theta + 90°) + 1 [/math] must be -2

The amplitude is the distance from the equilibrium to the extrema, and as such is a non-negative value. In the sinusoid you cite, the amplitude is defined as:

$$A=|-2|=2$$
 
MarkFL said:
The amplitude is the distance from the equilibrium to the extrema, and as such is a non-negative value. In the sinusoid you cite, the amplitude is defined as:

$$A=|-2|=2$$

Oh, I understand now. Thank you very much.
 

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