A marching band performs on the football field at half-time. As they perform, the members of the band stand in the shape of a sinusoidal function. While playing, they move, but still maintain the sinusoidal function, transforming it in different ways.

Darla is a member of the marching band. As the band begins to play she is positioned in the exact
center of the field. The person closest to her on the same horizontal line, stands 10 yards away. The sinusoidal function extends to the ends of the playing field.

The playing area of football field measure 300 feet by 160 feet. Place the playing area of a football
field on the coordinate plane such that the origin is the lower left corner of the football field.

1. What is the period and the amplitude of the sine function representing the position of
the band members as they begin to play?

2. Edna is sitting in the stands and is facing Darla. Edna observes that sine curve begins by
increasing at the far left of the field. What is the equation of the sine function
representing the position of band members as they begin to play?

3. As the band begins to play, band members move away from the edges, and the curve
reverses so that the function begins at the far left by decreasing. Darla does not move.
The sine curve is now half as tall as it was originally. What is the equation of the sine
curve representing the position of the band members after these changes?

4. Next, the entire band moves closer to the edge of the football field so that the sine curve
is in the lower half of the football field from Edna's vantage point. What is the equation
of the sine curve representing the position of the band members after these changes?