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

NameDate

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

On Ren's unit circle worksheet, θ is in Quadrant IV and sin θ = -7/25. What is cos θ?
On Zee's unit circle worksheet, θ is in Quadrant II and sin θ = 11/61. What is tan θ?
Esme's robot ends a turn θ in Quadrant III with cos θ = -33/65. What is tan θ?
4.
Jun writes sin 75° = sin(45° + 30°) = sin 45° cos 30° + cos 45° sin 30° on a worksheet. Which is the exact value of sin 75°?
- (√2 + 1)/2
- (√6 + √2)/4
- (√6 − √2)/4
- √2/2
5.
Kira writes cos 15° = cos(45° − 30°) = cos 45° cos 30° + sin 45° sin 30° from a math book. Which is the exact value of cos 15°?
- (√6 − √2)/4
- (√2 − √3)/2
- (√6 + √2)/4
- √2/2
6.
Luz writes sin 15° = sin(45° − 30°) = sin 45° cos 30° − cos 45° sin 30° on a worksheet. Which is the exact value of sin 15°?
- (√6 − √2)/4
- (√6 + √2)/4
- (√2 − 1)/2
- √2/2
7.
Milo writes cos 75° = cos(45° + 30°) = cos 45° cos 30° − sin 45° sin 30° from a math book. Which is the exact value of cos 75°?
- (√6 + √2)/4
- (√3 + √2)/2
- (√6 − √2)/4
- √2/2
On Noah's unit circle worksheet, the turn θ ends at (12/13, -5/13). What is sin(-θ) + cos(-θ)?
On Ren's unit circle worksheet, the turn θ ends at (-24/25, -7/25). What is cos(-θ) − sin(-θ)?
Tala's robot ends a turn θ at (9/41, 40/41) on a unit circle floor grid. What is sin(θ + 2π) + cos(-θ)?

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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