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# trigonometric function

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Throughout any given month, the maximum and minimum ocean tides follow a periodic pattern. Last year, at a certain location on the California coast, researchers recorded the height of low tide, with respect to sea level, each day during the month of July. The lowest low tide was first measured on July 11, at -1.4 feet. The highest low tide was first measured on July 4, at 1.8 feet. The average low tide for the month of July was measured to be 0.2 feet. write a function that it  represent the situstion ,

Nov 5, 2018

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We can represent this with a sine function [ cosine is also a possibility ].... we have the form

y = Asin (Bx + C) + D

The midline is at  [ 1.8 - 1.4] / 2  = 0.4/2 =   0.2 ft =  D

The amplitude is 1.6  =  A

The period is 14 days

B =   2pi/period  = 2pi/14  = pi/ 7

C  is the phase shift......this is the most difficult

We need to solve this  for C

Since we have a max at day 4,

pi (4)/7 +   C  =  pi/2

C = pi/2 - pi (4)/7    =    [7pi - 8pi  ] / 14  = -pi/14

So.....the function will be

y = 1.6sin ( pi * x / 7   - pi / 14) + 0.2

Where y is the tide height  on the " x th " day of the month

Here is a graph : https://www.desmos.com/calculator/pcvovyj5gs   Nov 5, 2018
edited by CPhill  Nov 5, 2018