7'6 Phase Shift Sinusoidal Curve Fitting

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7.6 Phase Shift Sinusoidal Curve Fitting
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The graphs of the sine and cosine functions are
called sinusoidal graphs.
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Theorem
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For the graphs of
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Find the amplitude, period, and phase shift of
the following function. Graph the function.
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(0,0)
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3
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-1
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Steps for Fitting Data to Sine Function y
Asin(wx - f)B

• Determine the amplitude
  A largest data value -2smallest data
  value
• Determine the vertical shift
  B
  largest data value 2 smallest data value
• Determine w from w2p/T.
• Determine the horizontal shift f by choosing an
  ordered pair (x, y) and solving the equation y
  Asin(wx - f)B

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The data on the following slide represent the
average monthly temperature in Houston, Texas.
(a) Draw a scatter diagram of the data treating
month as the independent variable.
(b) Find a sinusoidal function that fits the data.
(c) Graph the function found in (b) on your
scatter diagram.
(d) Find the sinusoidal function of best fit.
(e) Graph the function found in (d) on the
scatter diagram.
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Month
Average Temp (oF)
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Temperature
Month
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We will find a sinusoidal function of the form
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STEP 1 Determine the amplitude, A.
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STEP 2 Determine the vertical shift, B.
Vertical Shift
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STEP 3
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STEP 4 Determine the horizontal shift.
Use the first data x 1, y 50.
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To use a graphing utility to find the sine
function of best fit for the given data we will
use the SINe REGression program to get the
following