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Cogito

AP Calculus BC · Chapter 2 · Lesson 1

Practice Worksheet

Polar Coordinates

Locating a point by distance and angle.

11 problems · about 24 minutes · AP Calculus BC 9.7, 9.8

NameDate

Figure — use these to answer the problems

The angle gives the direction; cosine and sine give the coordinates.
(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.

4 problems

  1. Cartesian (6, 8). What is r?

    Answer

  2. r = 3, θ = 0°. What is y?

    Answer

  3. r = 4, θ = 90°. What is y?

    Answer

  4. Cartesian (3, 4). What is r?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Cartesian (0, 7). What is r?

    Answer

  2. r = 6, θ = 180°. What is x?

    Answer

  3. Set the angle to 270°, where cosine is 0 and sine is −1.

    Set the model in the app, then write the values you used.

Stretch Yourself

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

4 problems

  1. Does adding 360° to θ change the point? 1 for yes, 0 for no.

    Answer

  2. Cartesian (0, 0). What is r?

    Answer

  3. Straight Out

    r = 5, θ = 0°. What is x?

    Answer

  4. Straight Up

    r = 5, θ = 90°. What is x?

    Answer