Question

The depth d of water in a tank oscillates sinusoidally once every
4 hours. If the smallest depth is 7.9 feet and the largest depth is 10.1 feet, find a possible formula for the depth in terms of time t in hours. (Let the water depth be at the average when
t = 0.)

I got y=1.1cos(1/2pi t)
amplitude: (10.1-7.9)/2
B=2pi/4 = 1/2pi
No C because the water depth is at the midline when t=0?

but this was marked wrong

Answer 1

The depth at midline is 7.9+1.1 = 9.0

f(t) is at midline at t=0, so you want a sine function, not cosine, which starts at a max.

So, f(t) = 9.0 ± 1.1 sin(π/2 t)

I use ± because they don't say whether the water is rising or falling at t=0.

Answer 2

Thank you so much! That helped a lot!