A-Level Maths: Trigonometry Revision

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Does sin(2x) equal 2 sin(x)?

Trigonometry is a core part of A-Level Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.

Key concepts

Pythagorean identitysin²θ + cos²θ = 1 for all θ. Derived from the unit circle. Source of related identities.

tan identitytan θ = sin θ / cos θ. Undefined when cos θ = 0 (θ = π/2 + kπ).

Double angle formulaesin 2θ = 2 sin θ cos θ; cos 2θ = cos²θ − sin²θ = 1 − 2 sin²θ = 2 cos²θ − 1.

Sine & cosine rulesSine rule: a/sin A = b/sin B = c/sin C. Cosine rule: a² = b² + c² − 2bc cos A. Used in non-right triangles.

R cos(θ − α) forma cos θ + b sin θ = R cos(θ − α), where R = √(a² + b²), tan α = b/a. Useful for solving equations.

RadiansAngle measure where 2π rad = 360°. Arc length = rθ; area of sector = ½r²θ when θ in radians.

Tangent identitytan θ = sin θ / cos θ (where cos θ ≠ 0).

Double angle sinsin 2θ = 2 sin θ cos θ.

Double angle coscos 2θ = cos²θ - sin²θ = 1 - 2sin²θ = 2cos²θ - 1.

Double angle tantan 2θ = 2tanθ / (1 - tan²θ).

R formulaa sinθ + b cosθ = R sin(θ+α) with R=√(a²+b²).

Principal valueCalculator gives one solution; find others using symmetry.

sin periodsin x repeats every 360° (2π); has two solutions per cycle.

cos periodcos x repeats every 360°; symmetric about x=0.

What your exam board covers

Where Trigonometry sits in each exam board's specification. Tap a board to see what it lists.

AQATrigonometrySpec 7357

Part of: Pure mathematics

Source: AQA A-level Mathematics (7357) specification — Subject content, accessed 23 June 2026.

CCEATrigonometrySpec 2210

Part of: AS 1 — Pure mathematics

Source: CCEA A-Level Mathematics specification, accessed 23 June 2026.

EdexcelTrigonometrySpec 9MA0

Part of: Pure mathematics

Source: Pearson Edexcel A level Mathematics (9MA0) specification, accessed 23 June 2026.

OCRTrigonometrySpec H240

Part of: Pure mathematics

Source: OCR A Level Mathematics A (H240) specification, accessed 23 June 2026.

Learn Trigonometry step by step

Free interactive mini-lessons: short screens, worked examples and quick checks. Pick your exam board:

Common mistakes to avoid

Questions where students often pick the tempting wrong answer — make sure you know the right one:

Does sin(2x) equal 2 sin(x)?✗ Sin is a function, so sin(2x) = 2 sin(x) by pulling the constant out. ✓ No — sin is not a linear function; sin(2x) = 2 sin(x) cos(x).

What does sin^2(x) + cos^2(x) equal?✗ Sin^2(x) + cos^2(x) equals x because the trig functions cancel. ✓ 1 for all x — the Pythagorean trigonometric identity.

Practise Trigonometry — free games

Test yourself with these quick revision games for this topic:

▶ Two Truths, One Lie ▶ Reveal Race ▶ Connections Grid ▶ Falling Words ▶ Word Web

See all 22 games in the Revision Arcade →

Trigonometry

Key concepts

What your exam board covers

Common mistakes to avoid

Practise Trigonometry — free games

More A-Level Maths topics