trigonometric function questions

Question

Owen is jumping on a trampoline. When his feet hit the deck of the trampoline, the material depresses to a minimum height of 2cm. On average, Owen is reaching a maximum height of 200cm every 10 seconds. Determine the equation of a sinusoidal function that would model this situation, assuming Owen reaches his first maximum at 6 seconds.

Answer 1

Amplitude = (200-2)/2 so you know you will start out 99sin(bx+c)+d.

 

The period is 10.  Hmmm what is that formula about 2pi and period and b?

 

We know that the easy to find parts of the sine curve are where it starts, max, midpoint, min and of course, where it ends.  The curve is broken into 4 parts of equal length.  Since the period is 10, those lengths are 2.5 seconds long.  The first max is at 6 seconds.  6 - 2.5 = 3.5.  That must have something to do with that c.  What was that formula for phase shift?

 

There is also a vertical shift. That would be found by adding the amplitude to the minimum.

 

I hope this helps!  I will check your answer for you if you'd like.