Question

Wei is standing in wavy water and notices the depth of

the waves varies in a periodic way that can be modeled
by a trigonometric function. He starts a stopwatch to
time the waves.
After 1.1 seconds, and then again every 3 seconds, the
water just touches his knees. Between peaks, the water
recedes to his ankles. Wei's ankles are 12 cm off the
ocean floor, and his knees are 55 cm off the ocean floor.
Find the formula of the trigonometric function that
models the depth D of the water t seconds after Wei
starts the stopwatch. Define the function using
radians.

Answer 1

Answer:D(t)=21.5cos(2pi/3(t-1.1))+33

Explanation:

Answer 2

see the attachment

Explanation:

The function can be ...

D(t) = A +Bcos(C(t-p))

where A is the average depth (55+12)/2 = 33.5 cm,

B is the peak deviation from average, 55 -33.5 = 21.5 cm,

C is the horizontal scale factor (2π/T) = (2π/3) for a period (T) of 3 seconds,

and p is the phase offset, given as 1.1 seconds.

The function is ...

D(t) = 33.5 +21.5cos(2π/3·(t -1.1))