AP Precalculus: Inverse Trigonometric Functions (Drill 1)

About This Drill

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

Practice the domain and range restrictions that define arcsin, arccos, and arctan on the AP® Precalculus exam. Master evaluating inverse trig functions at standard values, composing trig with inverse trig, and applying inverse trig models to real-world contexts, all with careful attention to principal value ranges.

Questions in This Drill

1. What is the value of \( \arcsin\left(\dfrac{\sqrt{2}}{2}\right) \)?
2. What is the range of \( f(x) = \arctan(x) \)?
3. What is the value of \( \cos\!\left(\arcsin\!\left(\dfrac{3}{5}\right)\right) \)?
4. What is the domain of \( f(x) = \arccos(x) \)?
5. A drone flying horizontally is 500 meters from an observer and at a height of h meters. The angle of elevation from the observer to the drone is given by \( \theta = \arctan\!\left(\dfrac{h}{500}\right) \). If the angle of elevation is \( \dfrac{\pi}{6} \), what is the height of the drone?