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.
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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.
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