Question

Please help me with this!! Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide messures 5.15 ft at midnight, rises to a high of 10.2 ft, falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight.
What is the equation for f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation? Show your work and explain.

Answer 1

The amplitude is (10.2 - 5.15) or (5.15 - 0.1), which gives the same answer of 5.05 ft.
The period is 24 hours.
The initial value (at t = 0) is 5.15 ft.
The general equation for the sine wave is:
f(x) = (amplitude)*sin(x*2pi/period) + initial value
f(x) = 5.05*sin(x*pi/12) + 5.15