+0 I can really use some help. I am completely lost. It is multiple questions
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?
5. At the end of the performance, the band marches off the field to the right, moving the entire sine curve. Asa grabs his camera to takes a picture of the entire football field. At the instant he takes the picture, the first person forming the curve now stands at the 5 yard line. What is the equation of the sine curve representing the position of the band members in Asa's picture?
For question 1 I have amplitude=80 and the period =60
For question 2 I have 80sin( pi/30x-5pi)+80
For question 3 I have 40sin(pi/30x-5pi)+80
For question 4 I have 40sin(pi/30x-5pi)+40
For question 5 I have -65sin(pi/30x-5pi)+40
Nothing seems right except for question 1
i would appreciate any help
Thank -you
+1632 Yeah, there are a lot of questions here, so I'll leave you with this:
For a sin function\(f(x)=a\sin{(bx-c)}+d\) with parent function f(x) = sin(x), meaning all forms of the actual function are just transformations on sin(x):
1. Amplitude = |a|, if a < 0, vertical reflection of f(x)
2. Period (which means how long before the graph repeats itself) = 2pi/|b|, if b < 0, horizontal reflection of f(x)
3. Phase shift of c/b, and note that horizontal translations are generally the opposite of the sign.
4. + d refers to the increase/decrease proportionate to d's value of the midline; a vertical shift of f(x).
You can double check your answers or redo them with this information! :D
