Page 36 - Amplitude = M-m = 80 40 = 20 2 2 2 The midline of...

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Huynh, Kazyak, Rees, Ufner Page 36, #44 The desert temperature, H, oscillates daily between 40 ° F at 5am and 80 ° F at 5pm. Write a possible formula for H in terms of t, measured in hours from 5am. To find a formula, we first drew a graph. The general form of a sinusoidal function is f(x) = Asin(Bx)+c We know that the graph should start and end at 40 ° F. The graph’s maximum point should be at 80 ° F. Since the graph starts low, increases until 80 ° F, and then decreases back to 40 ° F, we know it is a negative cosine graph. The amplitude of the graph is the distance from the low or high point, to the midline.
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Unformatted text preview: Amplitude = M-m = 80 - 40 = 20 2 2 2 The midline of the graph is the halfway horizontal line between the high and low parts. To find it, you can subtract the amplitude from the highest point, or add the amplitude to the lowest point. Midline = M + m = 80 + 40 = 60 2 2 2 The period of the graph is the amount of time it takes for one full completion to be made. It takes 24 hours to begin and start at the same place (from 5am to 5am). Period = 2 Π = 24 IBI IBI Jon—graph here...
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