PencilGo

Grade 11 · Math · Algebra 2

11th grade The unit circle, and exact trig values of the special angles worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version
Print

The unit circle, and exact trig values of the special angles

Grade 11 Math Worksheet - Building Confidence

NameDate

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

  1. The point (-3/5, 4/5) in Quadrant II; an arrow across from the center (-3/5) and an arrow up (4/5). Luz marks the point (-3/5, 4/5) on a unit circle worksheet, at the end of a turn θ from the positive x-axis. What is cos θ?

  2. The point (5/13, -12/13) in Quadrant IV; an arrow across from the center (5/13) and an arrow up (-12/13). Milo's robot drives around a unit circle on a floor grid and stops at (5/13, -12/13) after a turn θ. What is sin θ?

  3. The point (-20/29, 21/29) in Quadrant II; an arrow across from the center (-20/29) and an arrow up (21/29). Pia's robot drives around a unit circle on a floor grid and stops at (-20/29, 21/29) after a turn θ. What is cos θ?

  4. Read this first

    Use this

    The 30-60-90 triangle with sides 1, √3 and 2; divide every side by 2 so the long side is the radius 1, then put it in the circle at 30°.

  6. Ren draws the 30° turn on a unit circle worksheet, with its 30-60-90 triangle. What is cos 30°?

    • √3/2
    • 1/2
    • √3
    • √2/2

  7. Tala's math book shows the 30° turn on the unit circle, with its 30-60-90 triangle. What is sin 30°?

    Use the picture in question 4.

    • √2/2
    • √3/2
    • 1
    • 1/2

  8. Zee draws the 45° turn on a unit circle worksheet, with its 45-45-90 triangle. What is sin 45°?

    • √3/2
    • 1/2
    • 1
    • √2/2

  9. Esme's math book shows the 60° turn on the unit circle, with its 30-60-90 triangle. What is cos 60°?

    • 1
    • √2/2
    • 1/2
    • √3/2

  11. Jun's robot starts at (1, 0) on a unit circle floor grid and turns 90° counterclockwise around the center. At which point does it stop?

  12. Kira turns a spinner arrow of length 1 through 180° from the positive x-axis. At which point does its tip stop?

    Use the picture in question 8.

  13. Milo turns a clock hand of length 1 through -270°, clockwise from the positive x-axis. At which point does its tip stop?

    Use the picture in question 8.

PencilGopencilgo.com

11th grade The unit circle, and exact trig values of the special angles worksheet – printable
Print: 123456

About this worksheet

The unit circle, and exact trig values of the special angles. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can read cos θ and sin θ from a point on the unit circle, with their signs.
  • I can give the exact values at 30°, 45° and 60° (π/6, π/4, π/3) and at the axis angles.
  • I can find the angle from a point on the unit circle, and mirror a special point into any quadrant.

Standard: F-TF.A.2, F-TF.A.3 (+)

Words to know

unit circle: A circle of radius 1 centered at (0, 0).

cosine (cos): The across value of the turn's point: its x-coordinate.

sine (sin): The up value of the turn's point: its y-coordinate.

tangent (tan): Up divided by across: sin θ ÷ cos θ.

exact value: A value with fractions and roots, like √3/2, not a decimal.

mirror point: The same point reflected across an axis or through the center.

Common mistakes

Swapped sine and cosine. Say together: the point is (cos, sin), across first, then up.

Lost the minus sign of a coordinate. Ask which way the arrow points, left or down, before writing the number.

Used the special triangle's sides (1, √3, 2) without shrinking them to fit a circle of radius 1. Ask what the long side must be.

Questions parents ask

What is the most common mistake with the unit circle, and exact trig values of the special angles?

Swapped sine and cosine. Say together: the point is (cos, sin), across first, then up.

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.

More algebra 2

See all Algebra 2

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records

Ready for easier practice?

Print a sheet, scan it when it’s done, and PencilGo picks the next one.

Create a free account