MHB How do you describe transformations in a sinusoid?

[mathdrama]

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

 

[MarkFL]

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.

 

[mathdrama]

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

 

[MarkFL]

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:

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

 

[mathdrama]

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.