Grade 11 · Math · Algebra 2

11th grade Angles in standard position: quadrants, coterminal and reference angles worksheet

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Angles in standard position: quadrants, coterminal and reference angles

Grade 11 Math Worksheet

NameDate

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

Kira's robot turns -5π/6 radians from the positive x-axis. Which angle from 0 to 2π radians ends at the same place?
Luz turns a spinner arrow -π/4 radians from the positive x-axis. Which angle from 0 to 2π radians ends at the same place?
Milo's bike wheel turns 31π/6 radians from the positive x-axis. Which angle from 0 to 2π radians ends at the same place?
Pia draws a turn of 5π/6 radians on a unit circle worksheet. What is its reference angle, in radians?
Ren's robot turns 4π/3 radians counterclockwise from the positive x-axis. What is the reference angle, in radians?
Tala turns a spinner arrow 5π/3 radians from the positive x-axis. What is the reference angle, in radians?
Esme's robot turns -150°, clockwise from the positive x-axis. What is the reference angle of the turn?
Jun's bike wheel turns 495° from the positive x-axis. What is the reference angle of the turn?
Kira turns a clock hand -240°, clockwise from the positive x-axis. What is the reference angle of the turn?
Luz spins a spinner arrow 590° from the positive x-axis. What is the reference angle of the turn?

11th grade Angles in standard position: quadrants, coterminal and reference angles worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Angles in standard position: quadrants, coterminal and reference angles. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can draw any angle as a turn from the positive x-axis and name its quadrant.
I can find an angle from 0° to 360° (or 0 to 2π) that ends at the same place.
I can find the reference angle of any angle, in degrees or radians.

Standard: F-TF.A.1, F-TF.A.2

Words to know

standard position: An angle that starts on the positive x-axis and turns from there.

counterclockwise: The turning direction of a positive angle: up first from the positive x-axis.

coterminal angles: Angles that end at the same place; they differ by full turns.

quadrant: One of the four parts of the grid, numbered I to IV counterclockwise.

reference angle: The acute angle between the end of the turn and the x-axis.

radian: The angle that cuts an arc one radius long; a full turn is 2π.

Common mistakes

Used a half turn (180° or π) as if it were a full turn. Turn around once on the spot together and count the 360°.

Turned the wrong way: a negative angle turns clockwise, a positive one counterclockwise. Act out a few turns with an arm pointing right.

Took away one full turn but stopped while the angle was still more than a turn. Ask which angle from 0° to 360° it lands on.

Questions parents ask

What is the most common mistake with angles in standard position: quadrants, coterminal and reference angles?

Used a half turn (180° or π) as if it were a full turn. Turn around once on the spot together and count the 360°.

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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