Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

AP Precalculus · Chapter 7 · Lesson 1

Practice Worksheet

Polar Coordinates

Locating a point by distance and direction.

12 problems · about 21 minutes · AP Precalculus 3.13, 3.14

NameDate

Figure — use these to answer the problems

The terminal point is the polar point with r = 1. Multiply both coordinates by r for any other distance.
(0.500, 0.866)
  • Angle60° = π/3 rad
  • x-coordinate0.500
  • y-coordinate0.866
  • cos 60°0.500
  • sin 60°0.866
Angle in degrees60
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. The rectangular point (8, 6). What is r?

    Answer

  2. What does r represent in a polar coordinate?

    • The distance from the origin.
    • The angle from the x-axis.

  3. (5, 90°) in polar. What is the y-coordinate?

    Answer

  4. (5, 90°) in polar. What is the x-coordinate?

    Answer

  5. The rectangular point (6, 8). What is r?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. (2, 180°) in polar. What is the x-coordinate?

    Answer

  2. The rectangular point (0, 7). What is θ in degrees?

    Answer

  3. (4, 270°) in polar. What is the y-coordinate?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Which polar pairs name the same point as (3, 30°)?

    • (3, 390 degrees)
    • (negative 3, 210 degrees)
    • (3, 60 degrees)
    • (30, 3 degrees)
    • Tick every box that applies.

  2. The rectangular point (−5, 0). What is r?

    Answer

  3. The Distance

    The rectangular point (3, 4). What is r?

    Answer

  4. The Coordinate

    The polar point (6, 0°). What is its x-coordinate?

    Answer