Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Trigonometry
Pythagoras and SOHCAHTOA on both tiers; the sine and cosine rules and full 3-D work at Higher.
Every lesson here ends the same way: learn it, teach it to an AI pupil who asks the awkward question, then defend it against the thinker with the strongest claim on it — free · no account needed.
4 modules of Pearson Edexcel International GCSE Mathematics (2 Higher Tier), each explained in full — what it is, why it works, when a question is asking for it, the mistakes that cost marks and worked examples — with five graded questions marked on your own device. Completely free.
The modules in Trigonometry
Pythagoras' Theorem
a² + b² = c² — finding missing sides in right-angled triangles, and spotting the hidden right triangles inside other shapes. In any RIGHT-ANGLED triangle, the square on the hypotenuse (the side opposite the right angle — always the longest) equals the sum of the squares on the other two sides: a² + b² = c².
When a question is asking for it: Two sides of a right triangle known, third wanted. Learn Pythagoras' Theorem →
Right-Angled Trigonometry
Sine, cosine and tangent: finding sides and angles in right triangles, from ladders to angles of elevation — plus the exact values worth knowing. In a right triangle, the ratios between sides depend only on the angle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent (SOH-CAH-TOA).
When a question is asking for it: One angle + one side known → label the sides relative to the angle (opposite/adjacent/hypotenuse), pick the ratio naming the two sides involved, solve. Learn Right-Angled Trigonometry →
The Sine & Cosine Rules (Higher Tier)
Trigonometry escapes the right angle: solving ANY triangle, plus the ½ab sin C area formula. Higher Tier. For any triangle with sides a, b, c opposite angles A, B, C: the sine rule a/sin A = b/sin B links opposite pairs; the cosine rule c² = a² + b² − 2ab cos C links three sides and the included angle.
When a question is asking for it: Choose by what you're given: an opposite PAIR in the mix → sine rule. Learn The Sine & Cosine Rules →
3-D Pythagoras & Trigonometry (Higher Tier)
Space diagonals, angles between lines and planes — finding the flat right-angled triangle hiding inside every solid. Higher Tier. 3-D problems are 2-D problems in disguise: every length or angle you need lives in some FLAT right-angled triangle inside the solid.
When a question is asking for it: Longest-rod-in-a-box questions; pyramid slant edges and slant faces; 'the angle between the diagonal and the base'. Learn 3-D Pythagoras & Trigonometry →
The mistakes that cost marks in Trigonometry
One from each module — the error examiners see most, with the module that puts it right.
- Adding the squares regardless. Finding a LEG subtracts: a² = c² − b². (Pythagoras' Theorem)
- Labelling 'opposite' relative to the wrong angle. Opposite and adjacent swap when you switch angles; the hypotenuse never moves. (Right-Angled Trigonometry)
- Using the cosine rule with a NON-included angle. The angle in c² = a² + b² − 2ab cos C must sit between a and b. (The Sine & Cosine Rules)
- Doing 3-D in one leap. Two clean 2-D steps beat one confused 3-D one — find the base diagonal first. (3-D Pythagoras & Trigonometry)
Where Trigonometry sits in the specification
Content area 4 of 4MA1, sub-topic 4.8. Incandio is aligned to the specification and is not published by Pearson; the numbers are given so you can check every module against your own copy.
- 4.8 — Pythagoras and trigonometry in three dimensions (Higher)
How Trigonometry is mastered on Incandio
Every module above ends the same way: five questions that climb Grade 6 → 9+, then you teach the method back to Ember, an AI pupil who asks the awkward question, and defend it against the mathematician with the strongest claim on it. Exam Ready carries 38 authored exam-style questions across this strand, marked on Incandio.
All of Incandio Mathematics · The 4MA1 specification · Exam Ready