# Sinusoidal function, find its parameters

1. Dec 11, 2011

### voltaire101

1. The problem statement, all variables and given/known data

Measurements of the height h(t) of water in a harbor are recorded ,where h is measured in meters and t in hours.It was noted that the rise and fall of a tide is modeled by a sinusoidal function giving the height by : h(t)=a+bsin(kt+c).

(a) Obtain values of the parameters a,b,c and k if measurement started when the level is equal to the mean level of 2.5 meters and has an amplitude of 1.5 meters and a period of 12 hours.

b) Compute the rate of change of the water height.

c) Find the highest and lowest values of h and the times at which they are taken.

2. Relevant equations

3. The attempt at a solution

This is a very complex problem (I think). OK, I tried to solve it in many way but with no progress, finally the doctor said that he will give us a hint. So I wrote this hint and I found it was very far from my attempts to solve it.

So I will type the doctor's hints..

at t=0 the height was 2.5

every 12 hours there is an amplitude of 1.5 meters

He also wrote this: (I don't know why he chose four periods)

when t=0 h=2.5
when t=12 h=4
when t=24 h=5.5
when t=36 h=7

when t=0 2.5=a+bsin(c)

when t=12 4=a+bsin(12k+c)

when t=24 5.5=a+bsin(24kc)

when t=36 7=a+bsin(36k+c)

for the first period:
sin(c)=$\frac{2.5-a}{b}$

for the second period:
sin(12k+c)=sin(12k)cos(c)+cos(12k)sin(c)

.... At this point I lost reception.

2. Dec 12, 2011

### Spinnor

Does this get you started?

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