AP Precalculus – Polar Coordinates & Polar Graphs – Drill 1

About This Drill

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

Practice converting between rectangular and polar coordinates and identifying polar graph families including roses, limaçons, cardioids, and circles. These AP® Precalculus questions cover Topics 3.13–3.14.

Questions in This Drill

1. A point has rectangular coordinates \( (3, 3) \). Which of the following gives the polar coordinates \( (r, \theta) \) of this point, where \( r > 0 \) and \( 0 \leq \theta < 2\pi \)?
2. A point has polar coordinates \( \left(4,\ \dfrac{2\pi}{3}\right) \). What are the rectangular coordinates \( (x, y) \) of this point?
3. Which of the following polar equations produces a limaçon?
4. The graph below shows one petal of the polar curve \( r = 4\cos(2\theta) \).
   
   
   
   Which of the following describes the complete graph of \( r = 4\cos(2\theta) \) for all \( \theta \in [0, 2\pi] \)?
5. A polar curve has the equation \( r = 2 + 2\cos\theta \). Which of the following statements is supported by the equation?