IGCSE Maths Trigonometry (SOH CAH TOA) Notes
Trigonometry links the sides and angles of triangles. SOH CAH TOA handles right angles; the sine and cosine rules handle any triangle.
Key concepts
- SOH CAH TOA
- sin = O/H, cos = A/H, tan = O/A for right-angled triangles.
- Sine rule
- Use with a matching side–angle pair in any triangle.
- Cosine rule
- Use for two sides and the included angle, or all three sides.
Key formulas
Sine rule
a/sin A = b/sin B = c/sin C
Cosine rule
a² = b² + c² − 2bc·cos A
Worked example
Find the angle whose opposite side is 5 and hypotenuse is 10.
- 1Use sin: sin x = opposite / hypotenuse = 5/10.
- 2sin x = 0.5.
- 3x = sin⁻¹(0.5).
Answer: x = 30°
Common mistakes
✗ Calculator set to radians.
✓ Use degrees mode for IGCSE trigonometry.
✗ Choosing the wrong ratio.
✓ Label the sides opposite, adjacent, hypotenuse relative to the angle first.
✗ Using SOH CAH TOA without a right angle.
✓ Switch to the sine or cosine rule for non-right triangles.
Quick check
Try these, then reveal the answers.
sin 30°?Reveal answer
0.5
Which ratio uses opposite and adjacent?Reveal answer
tan
Rule for three known sides?Reveal answer
Cosine rule
Exam tips
- Decide right-angled vs non-right-angled before choosing a method.
- Use the inverse functions (sin⁻¹ etc.) to find angles.
- Keep full accuracy in the calculator until the final answer.
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Frequently asked questions
When do I use SOH CAH TOA?+
For right-angled triangles, to find a missing side or angle from two known values.
How do I find an angle from a ratio?+
Use the inverse trig function, e.g. x = sin⁻¹(value), with the calculator in degrees.
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