General Form of Sine
Author: Scott Farrar

Observe how a, b, c, d affect the graph of the general form of sine.

f(x) = a * sin( b*x - c ) + d

Show Bounding Box

Questions:
1) What does each variable a, b, c, d do?
2) A period is defined as the distance it takes to complete one whole cycle.  Which variable controls the period?
3) Find an equation for the period.  P = 
4) Consider f(x) = 2 * sin ( π/4 * x + π/2 ) + 3.  Think about what the numbers will do to the graph,
      sketch it on paper, then check using the sliders.
5) The Bounding Box is a useful tool when graphing by hand.  Observe how 
      a, b, c, d affect it.
Extra Credit) Find Equations for the (x,y) coordinates of the four corners of the Bounding Box,
     (in terms of a, b, c, d, and f)

The General Form
of the Sine function

a = 1 (slider from -5 to 5, step 0.1)
d = 0 (slider from -5 to 5, step 0.1)
b = 1 (slider from -12 to 12, step 0.1)
c = 0 (slider from -12 to 12, step 0.1)
f(x) = a sin(b x - c) + d
A: (c / b, f(c / b) + a)
B: (c / b, f(c / b) - a)
C: (c / b + 2 * 3.14 / b, f(c / b) - a)
D: (c / b + 2 * 3.14 / b, f(c / b) + a)
poly1, a_1, b_1, c_1, d_1 = Polygon(A, B, C, D)
e = true