Grade 11 · Math · Precalculus

11th grade Polar equations and their graphs worksheet

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Polar equations and their graphs

Grade 11 Math Worksheet

NameDate

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

Milo sketches the rose r = 3 sin 4θ on polar graph paper. How many petals does it have?
Pia sketches the rose r = 2 cos 6θ on polar graph paper. How many petals does it have?
Tala sketches the rose r = 7 sin 5θ on polar graph paper. How many petals does it have?
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?
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?
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?
7.
Luz sees the polar graph shown. Which equation matches the graph?
- r = 6 cos θ
- r = -6 sin θ
- r = 6 sin θ
- r = 3 sin θ
8.
Milo sees the polar graph shown. Which equation matches the graph?
- r = 8 cos θ
- r = -4 cos θ
- r = -8 cos θ
- r = -8 sin θ
9.
Noah sees the polar graph shown. Which equation matches the graph?
- r = 3 + 3 sin θ
- r = 3 + 3 cos θ
- r = 6 + 6 sin θ
- r = 3 − 3 sin θ
10.
Pia sees the polar graph shown. Which equation matches the graph?
- r = 2 + 2 cos θ
- r = 4 − 4 cos θ
- r = 2 − 2 sin θ
- r = 2 − 2 cos θ

Polar equations and their graphs. Every version has 10 questions, and the answer key prints on the second page.

I can plot a polar point (r, θ), including a negative r, and fill a table of points for a polar equation.
I can read a polar circle, rose, cardioid, limaçon or spiral from its equation: size, petal count, side, inner loop.
I can match a polar graph to its equation (IXL X5).

Standard: none (beyond CCSS)

pole: The center point of a polar grid, the origin.

polar point (r, θ): Turn θ from the positive x-axis, then walk r.

rose: r = a sin nθ or a cos nθ: a flower of equal petals.

cardioid: r = a + a cos θ: a heart shape with its point at the pole.

spiral: r = cθ: the distance grows as the turning grows.

Read the polar point (r, θ) as if it were (x, y). Act it out together: turn to the angle first, then walk the distance.

Turned clockwise for the angle. Polar angles turn counterclockwise from the positive x-axis.

Used sine for x and cosine for y. x = r cos θ goes across, y = r sin θ goes up.

What is the most common mistake with polar equations and their graphs?

Read the polar point (r, θ) as if it were (x, y). Act it out together: turn to the angle first, then walk the distance.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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