Let Division be my Parent
Here in Purple is the graph y= (a sin (bx+c))/(a cos(bx+c)).
(sin x)/(cos x)= tan x is a Trig. Identity. Meaning it holds true for all values of x.
Thus, below, is the graph of the Tangent function.
The grey vertical lines are asymptotes. For tan x is undefined at pi/2 and 3pi/2.
Here the parent, the red curve, and the blue curve are all the same.
a is the value that affects the amplitude or range in this case.
The tangent function's range is -infinity<y<infinity.
The parent here is in purple(y= (sin bx)/ (cosbx)), where b=1.
In the red curve b=2 and in the blue curve b=0.5.
My earlier conjecture still holds true for the b-value.
Here are the graphs where the c-value has been changed.
However, as I mentioned before, (sin x)/ (cos x)= tan x is true no
matter what x-value you talk about. So it doesn't matter what you
add or subtract from the x-value, you will always get tan x.
Wow, it looks like my conjecture pretty much held true for the duration. Minus one little pesky composition function. How 'bout that?!
Sines and Cosines / Stu's Homepage / MTH 588