**WU
Number 1, Problem 5**
**David W. Stinson**

Examine graphs of the following function
for different values of *a,
b, c*

*y =a* sin(*bx + c*)
Begin by observing the parent graph *y*=
sin *x** *below:

A change in *a** *changes the **Altitude** (the vertical height
of the sin curve) such as illustrated below with *a*=
3. The maximum and minimum*
***y** values has been transformed
to **+/- 3**, respectively; from the parent altitude of **+/- 1 **(note:
when** ***a *< 0 then there is a reflection over a horizontal
axis).

To view Quick Time movie
click (**-5 < ***a *< 5) here.

The **Period** (length of time for
one complete cycle) of the function *y* =
sin b*x* is 360 degrees/*b*.
The function

*y *= sin 2*x*
now completes a full cycle in 180
degrees as opposed to 360 degrees as illustrated below:

To view Quick Time movie
click (**0 < ***b* < 5) here.

A change in *b* and *c*
will create a **Phase Shift**
(transformation to the right or left) in the sine function. In
the function* ***y**** = ***a* sin (*bx + c*) the phase shift is *-c/b*. If *c *>
0 the shift is to the left. If
*c *< 0,
the shift is to the right. This definition applies to all of the
trigonometric functions, illustrated below the function of *y*
= sin (*x* + 3.14), a shift
of 3.14 to the left:

To view Quick Time movie click (**-5 < ***c *< 5) here.

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