Below I have created my new Parent graph[y= ( a sin(bx+c))(a cos (bx+c))].
Conjecture: All the rules for how a, b, and c affect a y=sin x curve will apply to this new curve.
Here the purple curve is still the parent curve.
While in the red curve a=2 and in the black curve a=0.5
You can also see that the new amplitudes are actually 'a squared'.
Parent Graph in Purple.
While in the red curve b=2 and in the blue curve b=0.5
You can see, once again, that the original rules for the b-value are holding true.
Parent graph is purple.
In the red curve c=1.5 and in the blue curve c=0.5
Here the red curve and the blue curve are one in the same. They lie on top of each other.
Hmmmm?...
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