Asked by Julie
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 95 degrees occurs at 3 PM and the average temperature for the day is 80 degrees. Find the temperature, to the nearest degree, at 8 AM
Answers
Answered by
Steve
amplitude is (95-80)=15
center line is 80, so start with the assumption that the minimum occurs at midnight (0 hours):
y = -15cos(kx)+80
The function has a period of 24 hours, so 2?/k = 24, making k=?/12
y = -15cos(?/12 x) + 80
Now we know that the max occurs at x=15, not x=12, so we need to shift by 3:
y = -15cos(?/12 (x-3)) + 80
See the graph at
http://www.wolframalpha.com/input/?i=plot+-15cos(%CF%80%2F12+(x-3))+%2B+80++for+0%3C%3Dx%3C%3D24
center line is 80, so start with the assumption that the minimum occurs at midnight (0 hours):
y = -15cos(kx)+80
The function has a period of 24 hours, so 2?/k = 24, making k=?/12
y = -15cos(?/12 x) + 80
Now we know that the max occurs at x=15, not x=12, so we need to shift by 3:
y = -15cos(?/12 (x-3)) + 80
See the graph at
http://www.wolframalpha.com/input/?i=plot+-15cos(%CF%80%2F12+(x-3))+%2B+80++for+0%3C%3Dx%3C%3D24
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