You're viewing 1 free preview question for Maths AI HL — subscribe to unlock 6 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Trigonometric Functions · Paper 3 — Free Maths AI HL Practice Questions

1ChallengeLAQSine, cosine and tangent functions7 marksPaper 3~11 min
A Ferris wheel at an amusement park has a diameter of 40 m40\,\text{m}. The bottom of the wheel is 2 m2\,\text{m} above the ground. The wheel rotates at a constant speed, completing one full revolution every 6060 seconds. A rider boards the wheel at the lowest point when t=0t = 0 seconds. Let h(t)h(t) be the height of the rider above the ground, in metres, at time tt seconds.
(a)
Show that the height of the rider can be modelled by h(t)=22−20cos⁡ ⁣(πt30).h(t) = 22 - 20\cos\!\left(\frac{\pi t}{30}\right). [4 marks]
(b)
A second rider boards the wheel 1515 seconds after the first rider. Let h2(t)h_2(t) represent the height of the second rider above the ground at time tt seconds, where t=0t = 0 is the moment the first rider boards. (i) Explain why h2(t)=h(t−15)h_2(t) = h(t - 15). [2]
(ii) Find all times in the interval 0<t≤600 < t \leq 60 when both riders are at the same height. [4]
(iii) The first rider claims that, over one complete revolution (0≤t≤600 \leq t \leq 60), the two riders spend more time with the second rider higher than the first rider than vice versa. Determine whether this claim is correct, justifying your answer. [3 marks]
diagram

Solutions

Questions 2-7

Unlock these questions with Premium

Sign Up →

That's every free question here — 1 of 7.

+6 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade