MHB How do you describe transformations in a sinusoid?

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SUMMARY

The discussion clarifies that the amplitude of a sinusoidal function is always a non-negative value, defined as the absolute value of the coefficient in the function's equation. For the sinusoid represented by the equation $$f(x) = -2 \cos(3(\theta + 90°)) + 1$$, the amplitude is calculated as $$A = |-2| = 2$$. This means that despite the coefficient being negative, the amplitude itself is positive, reinforcing that amplitude is the distance from the equilibrium to the extrema.

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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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