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The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months since January 2001. (m = 0 represents January 2001.)

 

 May 14, 2020
 #1
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The following should help:

 

 May 14, 2020
 #2
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I'm not sure I understand fully..

Guest May 14, 2020
 #3
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Would that mean the amplitude is 24 and the vertical shift is 62? Then what would the period be?

Guest May 14, 2020
 #4
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A is the amplitude, which is half the vertical distance between the peak (86) and the trough (38).

 

The period, T, is 12 months.

 

The vertical shift is the y-value about which the sine curve oscillates i.e. it is the "middle" of the curve in the  vertical direction.

 

The offset angle of pi is there because the function starts going in the negative y-direction rather than positive y-direction.

 

Does this help?

Alan  May 14, 2020
 #5
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deleted..

Alan  May 14, 2020
edited by Alan  May 14, 2020

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