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.
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.
What is the mode of the data set [1, 2, 2, 3, 4, 4, 5]?✗ There is no mode because no single value is the most common. ✓ Both 2 and 4 — the data set is bimodal because two values occur most frequently.
If a data set has an extreme outlier, which average is most affected?✗ The median is most affected because the outlier shifts the middle. ✓ The mean — because every value (including the outlier) contributes to it.
What is the relationship between the angle at the centre and the angle at the circumference subtended by the same arc?✗ The angles are equal because they are subtended by the same arc. ✓ The angle at the centre is twice the angle at the circumference.
Practise Trigonometry — free games
Test yourself with these quick revision games for this topic:
See all 17 games in the Subjects Arcade →
More A-Level Maths topics
← All revision guides
Want to revise every topic this smart?
The Velvet Method teaches you to use AI to revise any subject — £25, lifetime access.
Explore the Course →