AP Precalculus – Trigonometric Equations – Drill 1

About This Drill

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

Practice solving trigonometric equations on restricted intervals using factoring, reciprocal functions, and sign-change analysis. These AP® Precalculus questions cover Topics 3.10–3.11.

Questions in This Drill

1. Which of the following gives all solutions to \( 2\sin^2\theta = -\sin\theta \) on \( [0, 2\pi) \)?
2. If \( \sec\theta = -2 \) and \( \dfrac{\pi}{2} < \theta < \pi \), what is the value of \( \sin\theta \)?
3. The table below shows selected values of \( g(x) = \sin(2.25x + 0.2) + 0.5 \) on the interval \( [0, \pi] \).
   
   

   x	0	1	1.5	2	2.5	3
   g(x)	1.198	0.270	−0.308	−0.387	0.297	0.997

   
   Based on the table, on which of the following intervals does \( g \) have a zero?
4. A Ferris wheel's height above the ground (in feet) is modeled by \( h(t) = 40\sin\!\left(\dfrac{\pi}{10}t\right) + 45 \), where \( t \) is time in seconds. During the first full revolution (\( 0 \leq t \leq 20 \)), for how many seconds is the rider at a height greater than 65 feet?
5. How many solutions does \( 2\cos^2\theta - \cos\theta - 1 = 0 \) have on the interval \( [0, 2\pi) \)?