Polar equations and their graphs

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Tala sorts limaçons, curves of the form r = a + b cos θ or r = a + b sin θ. Which equation's graph has an inner loop?

   • r = 2 + 5 cos θ
   • r = 4 + 4 cos θ
   • r = 5 + 2 cos θ
2. 2.

   Zee sorts limaçons, curves of the form r = a + b cos θ or r = a + b sin θ. Which equation's graph has an inner loop?

   • r = 5 − 3 sin θ
   • r = 3 − 3 sin θ
   • r = 3 − 5 sin θ
3. 3.

   Esme sorts limaçons, curves of the form r = a + b cos θ or r = a + b sin θ. Which equation's graph has an inner loop?

   • r = 1 + 3 sin θ
   • r = 3 + sin θ
   • r = 2 + 2 sin θ
4. 4.

   Jun sorts limaçons, curves of the form r = a + b cos θ or r = a + b sin θ. Which equation's graph has an inner loop?

   • r = 4 − 7 cos θ
   • r = 7 − 4 cos θ
   • r = 5 − 5 cos θ
5. 5.

   Luz graphs r = -6 cos θ, a circle through the pole. What is the center (x, y) of the circle?

   (-3, 0)
6. 6.

   Milo graphs r = 10 cos θ, a circle through the pole. What is the center (x, y) of the circle?

   (5, 0)
7. 7.

   Noah graphs r = -12 sin θ, a circle through the pole. What is the center (x, y) of the circle?

   (0, -6)
8. 8.

   A spiral path in a park follows r = 3θ m, θ in radians. Tala follows it 1 full turn from the center. In terms of π, how far out is it?

   6π
9. 9.

   A coiled clock spring follows r = 1.5θ mm, θ in radians. Zee follows it 3 full turns from the center. In terms of π, how far out is it?

   9π
10. 10.

    A coiled rope on a dock follows r = 4θ cm, θ in radians. Esme follows it half a turn from the center. In terms of π, how far out is it?

    4π