Here my new parent graph will be y= a sin (b(a cos(bx+c)+c), where a=b=1 and c=0.
The purple curve is the parent(y= a sin(a cos x)).
In the red curve a=2 and in the blue curve a= 0.5
The blue curve acts the way I would expect, only changing the amplitude.
However the red curve behaves oddly. Hmmm?
In the red curve a>1, giving it the different look. While the blue curve seems to keep the same look as the parent graph. The blue curve 0<a<1. Essentially my conjecture still holds true.
The a-value still only effects the amplitude of my new function.
I am getting the feeling that this is where my conjecture will start to break down. The parent equation is here in the purple(y= sin b(cos bx), where b=1). The b-value has done it's job once again. The b-value, in the red function(b=2), has sqeezed the picture together.
Now there are two cycles in the same distance as one of the parent graph.
The same holds true for the blue curve(b=0.5). Now there is a half a cycle in the same distance as one full parent cycle.
Here is where I beleive my conjecture must fall apart.
The parent graph is in Purple[ y= sin (cos (x+c)+c), where c=0].
My conjecture was that the c-value would simply shift all the points left and right. In the red and blue pictures it seems that the final c-value is actually shifting the picture up and down. I am not sure if that is just becuase NuCalc reads it that way or not. In the class that I teach we talk about a d-value that does move the picture up and down. It seems as if that is happening here.
Man, I was close to getting all the way through.
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