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Over a 24 hour period, the tide in a harbour can be modeled by one period of a sinusoidal function. The tide measures 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 the sine function f(x), Where x represents time in hours since the beginning of the 24 hour period, that models the situation?

 

f(x) = 

 Jan 28, 2019
 #1
avatar+103948 
+1

We have the form

 

f(x) = A sin (Bx) +  D

 

A = the amplitude =  [ highest point - lowest point] / 2 =  [ 10.2 - .1] / 2 = 10.1/2 = 5.05

 

The period is 24

 

B = 2pi / period =  2pi /24  =  pi/12

 

D = the midline =  (highest point + lowest point] ) / 2  =  (10.2 + 0.1) / 2 = 10.3 /2 = 5.15

 

So....the equation is

 

f(x) = 5.05sin [ (pi/12) x ] + 5.15

 

 

cool cool cool

 Jan 28, 2019

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