Grade 11 · Math · Algebra 2

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

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

Grade 11 Math Worksheet - Building Confidence

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

On Noah's unit circle worksheet, θ is in Quadrant II and sin θ = 3/5. What is cos θ?
Pia's robot ends a turn θ in Quadrant IV with cos θ = 5/13. What is sin θ?
On Ren's unit circle worksheet, θ is in Quadrant III and sin θ = -8/17. What is cos θ?
Tala's robot ends a turn θ in Quadrant II with cos θ = -20/29. What is sin θ?
Esme's robot ends a turn θ at (-3/5, 4/5) on a unit circle floor grid. Where does a turn of -θ end?
On Jun's unit circle worksheet, the turn θ ends at (-7/25, -24/25). Where does the turn -θ end?
Luz's robot ends a turn θ at (12/13, 5/13) on a unit circle floor grid. Where does a turn of 90° − θ end?
On Milo's unit circle worksheet, the turn θ ends at (3/5, 4/5). Where does the turn 90° − θ end?
Noah's robot ends a turn θ at (-15/17, 8/17) on a unit circle floor grid. Where does a turn of 90° − θ end?
On Pia's unit circle worksheet, the turn θ ends at (24/25, -7/25). Where does the turn 90° − θ end?

11th grade Trig identities: Pythagorean, symmetry and periodicity, and sum and difference worksheet – printable — Print: 1 2 3 4 5 6

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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