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IB Mathematics: Applications and Interpretation SL · 12.7: Mathematical Models · 12.7.2

Sinusoidal models: Ferris wheels, tides and daylight Problem set B Answers

Skills

    1. (a) \(h=-0.2\cos(240t)+0.32\)
    2. (b) 0.42 m
    1. (a) \(h=0.4\sin(180t)+0.8\)
    2. (b) 1.12 m
    1. (a) 0.793
    2. (b) 2.41

In context

    1. (a) \(h=-5\cos(18t)+5.8\)
    2. (b) 7.35 m
    3. (c) 8.46 seconds
    1. (a) \(D=1.7\sin(30t)+2.9\)
    2. (b) 4.54 m
    3. (c) 4.62 hours
    1. (a) \(T=-12\cos(30t)+6\)
    2. (b) 2.89 °C
    3. (c) 4.70 months
    4. (d) It repeats exactly every year. Real temperatures change from year to year.

Stretch

    1. (a) t = 6.54 and t = 11.5
    2. (b) 14.2 hours
    3. (c) The model repeats exactly every cycle. A real tide changes with the moon, the weather and the season.
    1. (a) \(h_1=-9\cos(30t)+10\) and \(h_2=9\sin(30t)+10\)
    2. (b) 4.5 minutes
    3. (c) 16.4 m

jmaths.xyz · AI SL · 12.7.2 Sinusoidal models: Ferris wheels, tides and daylight