GCSE Maths: Pythagoras and Trigonometry
Master GCSE Maths Pythagoras theorem and trigonometry (SOH-CAH-TOA) with practice questions for both Foundation and Higher tiers. AQA, Edexcel, OCR and Eduqas.
GeometryFoundation & HigherAQA · Edexcel · OCR · Eduqas
What you need to know
The concepts examiners test on pythagoras and trigonometry, and what each one is really asking.
Pythagoras theorem: a² + b² = c²
SOH-CAH-TOA for right-angled triangles
Finding missing sides and angles
Exact trigonometric values (30°, 45°, 60°)
Applications in 2D and 3D problems
Where marks get lost
The exam technique that separates a correct method from a correct answer.
- Pythagoras: longest side squared = sum of other two sides squared
- SOHCAHTOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj
- Use inverse trig (sin⁻¹, cos⁻¹, tan⁻¹) to find angles
Pythagoras and Trigonometry questions students ask
When do I use Pythagoras vs trigonometry?
Use Pythagoras when you know two sides and want the third — no angles needed. Use trigonometry when you have an angle and need a side, or have two sides and need an angle.
What are the exact trig values I need to know?
sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3; sin 45° = cos 45° = 1/√2; sin 60° = √3/2, cos 60° = ½, tan 60° = √3.