MHB How do you describe transformations in a sinusoid?

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Transformations in a sinusoid are described by the amplitude, which is always a positive value, representing the distance from the equilibrium to the extrema. The amplitude is calculated as the absolute value of the coefficient in front of the sine or cosine function, regardless of its sign. For example, in the function -2 cos(3(θ + 90°)) + 1, the amplitude is | -2 | = 2. It is clarified that the amplitude cannot be negative, and any confusion regarding negative values is addressed. Understanding this concept is crucial for accurately describing sinusoidal transformations.
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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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