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Grade 11 · Math · Algebra 2

11th grade Trig values by reference angle and quadrant sign, and the reciprocal ratios worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

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Trig values by reference angle and quadrant sign, and the reciprocal ratios

Grade 11 Math Worksheet - Challenge Me

NameDate

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

  1. Esme works out cos(7π/6) on a unit circle worksheet. What is cos(7π/6)?

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

  2. Jun's robot turns -4π/3 radians, clockwise, on a unit circle floor grid. What is cos(-4π/3)?

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

  3. Kira's math book asks for the exact value of tan(5π/3). What is tan(5π/3)?

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

  4. Luz works out sin(11π/6) on a unit circle worksheet. What is sin(11π/6)?

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

  5. Milo finds csc 220° on a calculator, to the nearest thousandth, for a unit circle worksheet. What is csc 220°?

  6. Noah's robot turns 2 radians, and Noah finds sec 2 on a calculator to the nearest thousandth. What is sec 2?

  7. Pia finds sec 290° on a calculator, to the nearest thousandth, for a unit circle worksheet. What is sec 290°?

  8. Ren's robot turns 3 radians, and Ren finds csc 3 on a calculator to the nearest thousandth. What is csc 3?

  9. Zee's math book asks for the exact value of sec(3π/4). What is sec(3π/4)?

    • √2
    • -√2/2
    • -√2
    • 2

  10. Esme works out cot(5π/6) on a unit circle worksheet. What is cot(5π/6)?

    • 2
    • √3
    • -√3
    • -√3/3
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11th grade Trig values by reference angle and quadrant sign, and the reciprocal ratios worksheet – printable
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About this worksheet

Trig values by reference angle and quadrant sign, and the reciprocal ratios. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can tell the signs of cos θ and sin θ from the quadrant.
  • I can find sin, cos and tan of any special angle from its reference angle and quadrant.
  • I can find csc, sec and cot as reciprocals, exactly or on a calculator in the right mode.

Standard: F-TF.A.2, F-TF.C.8 (related)

Words to know

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

cosecant (csc): 1 ÷ sin θ.

secant (sec): 1 ÷ cos θ.

cotangent (cot): cos θ ÷ sin θ, the flip of tan θ.

reciprocal: 1 divided by a number: the fraction flipped, same sign.

degree mode / radian mode: The calculator setting that says which unit an angle is in.

Common mistakes

Used the right size of value but the Quadrant I sign. Ask which quadrant the angle ends in, and whether its point is left or right, up or down.

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

Measured the reference angle to the y-axis. Ask which axis the reference angle always uses (the x-axis).

Questions parents ask

What is the most common mistake with trig values by reference angle and quadrant sign, and the reciprocal ratios?

Used the right size of value but the Quadrant I sign. Ask which quadrant the angle ends in, and whether its point is left or right, up or down.

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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