AP® Precalculus – Sinusoidal Function Models – Drill 1

About This Drill

AP® Precalculus – Sinusoidal Function Models – Drill 1 is a Math practice drill covering Sinusoidal Function Models. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice constructing and interpreting sinusoidal models for real-world periodic phenomena, from Ferris wheels to rotating machinery. Master the critical relationship between rotational rate and angular frequency — and avoid the common trap of using the rotation count directly as ω instead of computing 2π divided by the period.

Questions in This Drill

1. The height, in feet, of a rider on a Ferris wheel is modeled by \( h(t) = 40\cos\!\left(\dfrac{\pi t}{15}\right) + 45 \), where t is measured in seconds. Which of the following statements about the rider is true?
2. A waterwheel completes 3 full rotations per minute. A point on the rim of the wheel has its vertical position modeled by a sinusoidal function of time. What is the angular frequency ω (in radians per minute) of the model?
3. A bicycle pedal arm rotates at a constant rate of 1 revolution per second. At t = 0, the pedal is at its highest point, 14 inches from the center of rotation. The center of rotation is 10 inches above the ground. Which of the following correctly models the height h (in inches) of the pedal above the ground at time t seconds?
4. The table below shows selected values of a sinusoidal function f(t).
   
   

   t (sec)	0	3	6	9	12
   f(t) (ft)	7	13	7	1	7

   
   Which of the following statements is supported by the table?
5. A buoy's height h (in meters) above the seafloor is modeled by \( h(t) = -5\sin\!\left(\dfrac{\pi t}{6}\right) + 9 \), where t is in seconds. A second buoy has the same amplitude and midline as the first buoy but twice the period. Which equation models the second buoy?