Polar equations and their graphs

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Milo sketches the rose r = 3 sin 4θ on polar graph paper. How many petals does it have?

   8
2. 2.

   Noah sketches the rose r = 5 cos 3θ on polar graph paper. How many petals does it have?

   3
3. 3.

   Tala sketches the rose r = 7 sin 5θ on polar graph paper. How many petals does it have?

   5
4. 4.

   A microphone picks up sound in the cardioid pattern r = 5 + 5 cos θ, in meters. Zee reads the polar graph. What is the largest value of r?

   10
5. 5.

   A garden light shines in the pattern r = 4 + 6 sin θ, in meters. Jun reads the polar graph. What is the largest value of r?

   10
6. 6.

   A speaker sends sound in the pattern r = 6 − 2 cos θ, in meters. Kira reads the polar graph. What is the largest value of r?

   8
7. 7.

   Luz sees the polar graph shown. Which equation matches the graph?

   • r = -6 sin θ
   • r = 3 sin θ
   • r = 6 sin θ
   • r = 6 cos θ
8. 8.

   Milo sees the polar graph shown. Which equation matches the graph?

   • r = -8 cos θ
   • r = -8 sin θ
   • r = -4 cos θ
   • r = 8 cos θ
9. 9.

   Noah sees the polar graph shown. Which equation matches the graph?

   • r = 3 + 3 cos θ
   • r = 3 − 3 sin θ
   • r = 6 + 6 sin θ
   • r = 3 + 3 sin θ
10. 10.

    Pia sees the polar graph shown. Which equation matches the graph?

    • r = 2 − 2 sin θ
    • r = 2 − 2 cos θ
    • r = 2 + 2 cos θ
    • r = 4 − 4 cos θ