Grade 11 · Math · Precalculus

11th grade Polar equations and their graphs worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Polar equations and their graphs

Grade 11 Math Worksheet - Building Confidence

NameDate

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

1.
Esme plots the polar point (4, 90°): turn 90° counterclockwise, then walk r = 4. Which (x, y) point is it?
- (0, -4)
- (0, 4)
- (4, 0)
- (4, 90)
2.
Jun plots the polar point (-3, 180°): turn 180° counterclockwise, then walk r = -3. Which (x, y) point is it?
- (3, 0)
- (0, 3)
- (-3, 180)
- (-3, 0)
3.
Kira plots the polar point (5, 270°): turn 270° counterclockwise, then walk r = 5. Which (x, y) point is it?
- (-5, 0)
- (0, -5)
- (5, 270)
- (0, 5)
4.
Luz plots the polar point (-2, 90°): turn 90° counterclockwise, then walk r = -2. Which (x, y) point is it?
- (0, 2)
- (0, -2)
- (-2, 90)
- (-2, 0)
Milo makes a table of points for r = 5 + 3 cos θ. What is r when θ = 180°?
Noah makes a table of points for r = 1 + 4 cos θ. What is r when θ = 120°?
Tala makes a table of points for r = 8 cos 3θ. What is r when θ = 60°?
Zee makes a table of points for r = 12 cos 2θ. What is r when θ = 60°?
Esme makes a table of points for r = 6 cos 2θ. What is r when θ = 90°?
Jun graphs r = 8 cos θ, a circle through the pole. What is the radius of the circle?

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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