AP® Precalculus – Periodic Phenomena and Unit Circle – Drill 21

About This Drill

AP® Precalculus – Periodic Phenomena and Unit Circle – Drill 21 is a Math practice drill covering Periodic Phenomena and Unit Circle. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

This AP(r) Precalculus drill covers periodic phenomena and the unit circle (Topics 3.1-3.2): identifying period, amplitude, and midline from graphs and tables; understanding radian measure; and using the unit circle to evaluate sine and cosine at key angles. These foundational skills underpin all of Unit 3.

Questions in This Drill

1. A periodic function \( f \) has the following property: starting at \( x = 0 \), the function reaches its maximum value at \( x = 1 \), returns to its starting value at \( x = 2 \), reaches its minimum value at \( x = 3 \), and returns to its starting value and rate of change at \( x = 4 \). The pattern then continues to repeat. What is the period of \( f \)?
2. Which of the following quantities is best described as periodic?
3. What is the exact value of \( \cos\!\left(\dfrac{5\pi}{6}\right) \)?
4. The table below shows the temperature \( T \) (in degrees Fahrenheit) inside a greenhouse at time \( t \) hours after midnight, recorded over a 6-hour window. The temperature pattern is periodic.

   t (hours)	0	1	2	3	4	5	6
   T (°F)	62	71	68	59	62	71	68

   What is the period of the temperature function?
5. A Ferris wheel has a radius of 20 meters, and its center is 25 meters above the ground. The wheel completes one full revolution every 40 seconds. A rider begins at the lowest point of the wheel at time \( t = 0 \) seconds. Which of the following expressions gives the rider's height \( h(t) \) in meters above the ground at time \( t \) seconds?