IGCSE Maths Geometry & Trigonometry Notes
IGCSE geometry combines angle rules, Pythagoras and trigonometry, extending to the sine and cosine rules for non-right-angled triangles.
Key concepts
- SOH CAH TOA
- Right-angled trig ratios linking sides and angles: sin, cos and tan.
- Sine rule
- For any triangle, relates each side to the sine of its opposite angle.
- Cosine rule
- Finds a side from two sides and the included angle, or an angle from three sides.
Key formulas
Sine rule
a/sin A = b/sin B = c/sin C
Cosine rule
a² = b² + c² − 2bc·cos A
Area of a triangle
Area = ½·ab·sin C
Worked example
A right-angled triangle has opposite 6 cm and angle 30°. Find the hypotenuse.
- 1Use sin: sin 30° = opposite / hypotenuse.
- 2Rearrange: hypotenuse = 6 / sin 30°.
- 3sin 30° = 0.5, so hypotenuse = 6 / 0.5.
Answer: 12 cm
Common mistakes
✗ Using SOH CAH TOA on a non-right-angled triangle.
✓ Use the sine or cosine rule when there is no right angle.
✗ Calculator in radians mode.
✓ Set the calculator to degrees for IGCSE trigonometry.
✗ Choosing the wrong rule.
✓ Two sides + included angle → cosine rule; a side–angle pair → sine rule.
Quick check
Try these, then reveal the answers.
tan 45° = ?Reveal answer
1
Which rule for two sides and the angle between them?Reveal answer
Cosine rule
Area formula using two sides and included angle?Reveal answer
½·ab·sin C
Exam tips
- Label the sides a, b, c opposite their angles A, B, C before choosing a rule.
- Keep full calculator accuracy until the final rounding step.
- Check the answer is sensible — the longest side faces the largest angle.
Related practice
Practise this topic
Exam-style questions with instant Study Coach feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Study Coach
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Key terms explained
Short, exam-ready definitions with a formula, a worked example and an examiner tip.
Frequently asked questions
When do I use the sine rule versus the cosine rule?+
Use the sine rule with a matching side–angle pair; use the cosine rule for two sides and the included angle, or three sides.
Is trigonometry on both IGCSE papers?+
Yes — trigonometry appears across the IGCSE Maths papers and is a reliable source of marks with clear working.
Create a free account to practise geometry & trigonometry with Study Coach feedback
Try 5 questions now, get instant examiner-grade marking and ask the Study Coach to explain anything. Free during our early launch period — no credit card required.
Related on MathsGradeUp
Keep studying
- Mathematics courses & specifications
Every board and level we cover for mathematics.
- Formula sheets
Every GCSE, IGCSE and A Level formula, searchable and explained.
- Maths & science glossary
Plain-English definitions with a formula, worked example and examiner tip.
- Free maths calculators & solvers
Step-by-step solvers for the calculations that come up in every paper.
- Past paper guides
Paper structure, timings and topic weightings board by board.
- Grade boundaries
Historic boundaries and what each grade typically needs.
- Browse subjects
Specification-mapped courses for every board and level.
Practise it
- Predicted papers
GCSE and A Level predicted papers with full mark schemes.
- Question bank
Filter thousands of exam-board questions by topic and difficulty.
- Past papers workspace
Write on real papers and get every line marked.