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Grade 11 · Math · Algebra 2

11th grade Trig identities: Pythagorean, symmetry and periodicity, and sum and difference worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

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Trig identities: Pythagorean, symmetry and periodicity, and sum and difference

Grade 11 Math Worksheet - Challenge Me

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

  1. On Esme's unit circle worksheet, turn A ends at (-4/5, 3/5) and turn B ends at (12/13, -5/13). What is cos(A − B)?

  2. Jun's robot turns A, ending at (8/17, 15/17); a turn of B alone ends at (-3/5, 4/5). Then the robot turns B more. What is sin(A − B)?

  3. On Luz's worksheet, sin A = 4/5 with A in Quadrant II, and sin B = 5/13 with B in Quadrant I. What is cos(A + B)?

  4. Milo's robot makes two turns: cos A = -12/13 with A in Quadrant III, and cos B = 3/5 with B in Quadrant IV. What is sin(A − B)?

  5. On Noah's worksheet, sin A = -3/5 with A in Quadrant IV, and cos B = -5/13 with B in Quadrant III. What is sin(A + B)?

  6. Pia's robot makes two turns: cos A = 5/13 with A in Quadrant IV, and sin B = 4/5 with B in Quadrant II. What is cos(A − B)?

  7. Ren solves sin x cos 30° + cos x sin 30° = 1/2 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

  8. Tala's math book asks for every x with cos x cos 45° − sin x sin 45° = 0 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

  9. Zee solves sin x cos 60° − cos x sin 60° = 0 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

  10. Esme's math book asks for every x with cos x cos 30° + sin x sin 30° = 1/2 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

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11th grade Trig identities: Pythagorean, symmetry and periodicity, and sum and difference worksheet – printable
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About this worksheet

Trig identities: Pythagorean, symmetry and periodicity, and sum and difference. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find cos θ from sin θ and the quadrant with x² + y² = 1.
  • I can find the points and values for -θ, 90° − θ and θ + 2π by mirrors and full turns.
  • I can use the sum and difference formulas to find exact values and solve equations.

Standard: F-TF.C.8, F-TF.A.4 (+), F-TF.C.9 (+)

Words to know

identity: An equation that is true for every angle, like sin² θ + cos² θ = 1.

Pythagorean identity: x² + y² = 1 on the unit circle: cos² θ + sin² θ = 1.

even / odd: cos(-θ) = cos θ (even); sin(-θ) = -sin θ (odd).

period: The turn after which values repeat: 2π (360°) for sin and cos.

cofunction: sin(90° − θ) = cos θ: the mirror across y = x swaps across and up.

sum formula: sin(A + B) = sin A cos B + cos A sin B: two turns in a row.

Common mistakes

Found the right size but missed the sign the quadrant gives. Ask whether the point is left or right, up or down.

Stopped at cos² θ (or sin² θ) and did not take the square root. Ask what number squared gives that fraction.

Took the value away from 1 before squaring it. In x² + y² = 1, square first, then subtract.

Questions parents ask

What is the most common mistake with trig identities: pythagorean, symmetry and periodicity, and sum and difference?

Found the right size but missed the sign the quadrant gives. Ask whether the 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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