A-Level Trigonometry Revision
Trigonometry revision for A-Level and International A-Level Maths
Trigonometry at A-Level is less about the triangles and more about the identities. Most of the marks sit in rearranging an expression into a form you can actually solve — recognising that a stubborn equation becomes straightforward once you apply a double angle formula, or that a mixture of sine and cosine can be collapsed into a single R sin(θ + α). This free revision engine covers the trigonometry content of Edexcel A-Level Maths and the International A-Level Pure 1 to Pure 3 papers, and works in radians throughout for the topics that require it.
What the trigonometry revision engine covers
The sine and cosine rules — including the ambiguous case Trigonometric ratios and exact values — the 30, 45 and 60 degree results without a calculator Trigonometric graphs and transformations — amplitude, period, and translations of sin, cos and tan Radians, arcs and sectors — arc length, sector area and segment area Solving trigonometric equations — finding every solution in a given range Trigonometric identities — using sin²θ + cos²θ = 1 and tan θ = sin θ / cos θ Reciprocal trigonometric functions — sec, cosec and cot, and their identities Inverse trigonometric functions — arcsin, arccos and arctan, and their restricted ranges The addition formulae — sin(A ± B), cos(A ± B) and tan(A ± B) The double angle formulae — sin 2θ, cos 2θ in its three forms, and tan 2θ R sin(θ + α) form — combining a sine and a cosine into a single wave Further trigonometric equations — those needing an identity before they can be solved
Trigonometry formulas you need to know
The sine rule. a / sin A = b / sin B = c / sin C. Watch for the ambiguous case when you are given two sides and a non-included angle. The cosine rule. a² = b² + c² − 2bc cos A. Area of a triangle. Area = ½ab sin C. The Pythagorean identity. sin²θ + cos²θ = 1, and dividing through gives 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ. Radians. 180° = π radians. Arc length s = rθ and sector area = ½r²θ, both with θ in radians. The addition formulae. sin(A ± B) = sin A cos B ± cos A sin B, and cos(A ± B) = cos A cos B ∓ sin A sin B. The double angle formulae. sin 2θ = 2 sin θ cos θ, and cos 2θ = 2cos²θ − 1 = 1 − 2sin²θ = cos²θ − sin²θ. R form. a sin θ + b cos θ = R sin(θ + α), where R = √(a² + b²) and tan α = b/a. The maximum value is R.
How to use it
Select a topic or an exam module and the engine generates a question. Answers are marked mathematically rather than by string matching, so an exact surd, a decimal and an equivalent rearrangement all count as correct, and a list of solution angles is accepted in any order. Two hints per question point you towards the right identity without giving the answer away.
More A-Level Maths revision
Trigonometry connects to several other topics: the R form appears again in modelling questions, and trigonometric integrals depend on knowing your identities well enough to rewrite an integrand. Track your progress across all topics on the revision hub. Everything here is free to use.