Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/mathematical-models/12-7-3/problems/

jmaths

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

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

Skills

    1. (a) \(h=-3\cos(0.524t)+3.5\)
    2. (b) 5 m
    1. (a) \(h=2.4\sin(1.26t)+5\)
    2. (b) 7.28 m
    1. (a) 1.35
    2. (b) 3.58
    1. (a) c = −0.667
    2. (b) \(P=6\sin(0.785(t+0.667))+20\)

In context

    1. (a) \(h=-20\cos(1.05t)+23\)
    2. (b) 40.3 m
    3. (c) 2.32 minutes
    1. (a) \(D=2.4\sin(0.507t)+4.8\)
    2. (b) 6.84 m
    3. (c) 5.03 hours
    1. (a) \(T=-10\cos(0.524t)+12\)
    2. (b) 14.6 °C
    3. (c) 4.84 months
    4. (d) It repeats exactly every year. Real temperatures change from year to year.
    1. (a) c = 0.993
    2. (b) \(h=18\sin(0.698(t-0.993))+19.5\)

Stretch

    1. (a) t = 7.14 and t = 11.5
    2. (b) 15.4 hours
    3. (c) The model repeats exactly every cycle. A real tide changes with the moon, the weather and the season.
    1. (a) \(h_1=-15\cos(0.785t)+17\) and \(h_2=15\sin(0.785t)+17\)
    2. (b) 3 minutes
    3. (c) 27.6 m

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