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IB Mathematics: Applications and Interpretation HL · 12.7: Mathematical Models · 12.7.3

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

Skills

    1. (a) \(h=-0.2\cos(4.19t)+0.32\)
    2. (b) 0.42 m
    1. (a) \(h=0.4\sin(3.14t)+0.8\)
    2. (b) 1.12 m
    1. (a) 0.779
    2. (b) 2.37
    1. (a) c = 0.655
    2. (b) \(P=5\sin(0.628(t-0.655))+15\)

In context

    1. (a) \(h=-5\cos(0.314t)+5.8\)
    2. (b) 7.35 m
    3. (c) 8.46 seconds
    1. (a) \(D=1.7\sin(0.524t)+2.9\)
    2. (b) 4.54 m
    3. (c) 4.62 hours
    1. (a) \(T=-12\cos(0.524t)+6\)
    2. (b) 2.89 °C
    3. (c) 4.70 months
    4. (d) It repeats exactly every year. Real temperatures change from year to year.
    1. (a) c = −0.327
    2. (b) \(h=10\sin(1.26(t+0.327))+11\)

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) \(h_1=-9\cos(0.524t)+10\) and \(h_2=9\sin(0.524t)+10\)
    2. (b) 4.5 minutes
    3. (c) 16.4 m

jmaths.xyz · AI HL · 12.7.3 Sinusoidal models: Ferris wheels, tides and daylight