Grade 11 · Math · Algebra 2

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

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

Grade 11 Math Worksheet

NameDate

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

1.
Noah fills in a unit circle worksheet at π/3 radians. What is sin(π/3)?
- 1/2
- √3
- √2/2
- √3/2
2.
Pia's math book asks for the exact value of cos(π/4). What is cos(π/4)?
- 1
- √3/2
- 1/2
- √2/2
3.
Ren fills in a unit circle worksheet at π/6 radians. What is tan(π/6)?
- √2/2
- √3/3
- √3/2
- √3
4.
Tala's math book asks for the exact value of tan(π/3). What is tan(π/3)?
- √3
- √3/3
- √2/2
- √3/2
5.
Zee fills in a unit circle worksheet at π/6 radians. What is cos(π/6)?
- 1/2
- √3
- √3/2
- √2/2
Esme's robot drives around a unit circle on a floor grid and stops at (7/25, -24/25) after a turn θ. What is tan θ?
Kira's robot drives around a unit circle on a floor grid and stops at (-15/17, -8/17) after a turn θ. What is tan θ?
Luz marks the point (-9/41, 40/41) on a unit circle worksheet, at the end of a turn θ. What is tan θ?
9.
Noah turns a spinner arrow of length 1 through π/4 radians from the positive x-axis. At which point does its tip stop?
- (√3/2, 1/2)
- (1, 1)
- (√2/2, √2/2)
- (1/2, √3/2)
10.
Pia's robot starts at (1, 0) on a unit circle floor grid and turns π/3 radians counterclockwise. At which point does it stop?
- (√3/2, 1/2)
- (1/2, √3/2)
- (√2/2, √2/2)
- (1, √3)

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.

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 (+)

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.

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.

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.

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