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Cogito

AP Precalculus · Chapter 7 · Lesson 2

Practice Worksheet

Graphs of Polar Functions

Curves that are simple only in polar form.

12 problems · about 21 minutes · AP Precalculus 3.14, 3.15

NameDate

Figure — use these to answer the problems

Sweep the angle through a full turn and imagine r changing as you go. That sweep is how a polar curve is traced.
(1, 0)
  • Angle0° = 0 rad
  • x-coordinate1
  • y-coordinate0
  • cos 0°1
  • sin 0°0
Angle in degrees0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. r = 5 cos(3θ). How many petals?

    Answer

  2. What curve does r = 8 draw?

    • A circle of radius 8.
    • A horizontal line at y = 8.

  3. r = 3 cos(5θ). How many petals?

    Answer

  4. r = 3 cos(2θ). How many petals?

    Answer

  5. r = 9. What is the radius?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. r = 5 cos(7θ). How many petals?

    Answer

  2. r = 4 cos(6θ). How many petals?

    Answer

  3. r = 3 + 3 cos θ. Is it a cardioid? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Match each polar equation with its curve.

    Draw a line from each item on the left to its match on the right.

    • r = 6
    • theta = 45 degrees
    • r = theta
    • A circle
    • A line through the origin
    • A spiral

  2. r = 4 cos(3θ). What is r at θ = 0°?

    Answer

  3. The Petals

    r = 2 cos(4θ). How many petals?

    Answer

  4. The Circle

    r = 7. What is the radius of this circle?

    Answer