Year 13 in England

12th grade trigonometry

7 12th grade trigonometry skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.

Mixed review

Ten questions drawn from every skill below.

Print a review worksheet Riddle puzzle on screen Bingo

Graphs of sine and cosine: amplitude and period

CCSS HSF.TF.B.5CCSS HSF.IF.C.7.E

Example

What is the period, in degrees, of y = 3 cos(2x)?

360° ÷ 2 = 180°

Answer: 180

Builds on: The unit circle and radians, Transformations of functions

Leads to: Read amplitude, period and midline from y = a sin(bx) + d

Print a worksheet ✏️ Write on screen Flashcards

Solve trigonometric equations

CCSS HSF.TF.B.7

Example

Solve sin x = √2/2 for 0° ≤ x < 360°. Give the smaller solution in degrees.

x = 45° or x = 135°

Answer: 45

Builds on: The unit circle and radians, Find angles with inverse trig

Leads to: Solve trigonometric equations between 0° and 360°

Print a worksheet ✏️ Write on screen Flashcards

Trigonometric identities

CCSS HSF.TF.C.8

Example

θ is acute and sin θ = 7/25. Find cos θ.

cos²θ = 1 − (7/25)² = 576/625
cos θ = 24/25

Answer: 24/25

Builds on: The unit circle and radians

Leads to: Use sin²θ + cos²θ = 1 to find exact values

Print a worksheet ✏️ Write on screen Flashcards

Read amplitude, period and midline from y = a sin(bx) + d

CCSS HSF.TF.B.5CCSS HSF.IF.C.7.EEngland: A-level Pure Mathematics

Example

For y = 5cos(3x) − 3 (x in degrees), what is the midline value (y = ?)?

y = −3

Answer: -3

Builds on: Graphs of sine and cosine: amplitude and period

Print a worksheet ✏️ Write on screen Flashcards

Use sin²θ + cos²θ = 1 to find exact values

CCSS HSF.TF.C.8England: A-level Pure Mathematics

Example

θ is acute and sin θ = 8/17. Find cos θ as a fraction.

1 − (8/17)² = 225/289
cos θ = 15/17

Answer: 15/17

Builds on: Trigonometric identities, Decide the sign of sin, cos and tan in each quadrant

Leads to: Simplify trigonometric expressions with identities

Print a worksheet ✏️ Write on screen Flashcards

Simplify trigonometric expressions with identities

CCSS HSF.TF.C.8England: A-level Pure Mathematics

Example

Simplify: 1 − cos²x

sin²x

Answer: sin²x

Builds on: Use sin²θ + cos²θ = 1 to find exact values

Print a worksheet ✏️ Write on screen Flashcards

Solve trigonometric equations between 0° and 360°

CCSS HSF.TF.B.7England: A-level Pure Mathematics

Example

Solve sin x = −√2/2 for 0° ≤ x < 360°.

Reference angle 45°
225°, 315°

Answer: 225°, 315°

Builds on: Use reference angles for angles beyond 90°, Solve trigonometric equations

Print a worksheet ✏️ Write on screen Flashcards

Keep exploring

Math, English and science that click.