Trigonometry SOHCAHTOA is one of the most searched IGCSE maths topics because right-angled trigonometry appears in almost every paper. SOHCAHTOA reminds you which ratio to use: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.

When to Use Each Ratio

• Finding a side: Identify the side you want and the side you know; choose the ratio that includes both (e.g. opposite and hypotenuse → sin).
• Finding an angle: Use the inverse function (sin⁻¹, cos⁻¹, tan⁻¹) after writing the ratio.
• Label the triangle – Mark opposite, adjacent and hypotenuse relative to the angle you are using.

Always work with the angle in degrees (check your calculator mode) and give answers to the accuracy asked (e.g. 3 significant figures).

Common Mistakes to Avoid

• Using the wrong ratio (e.g. using sin when you have opposite and adjacent).
• Confusing opposite and adjacent for the angle in question.
• Forgetting to use inverse trig when finding an angle.

Practise with past paper trigonometry questions so you can spot when to use SOHCAHTOA and when to use Pythagoras or other geometry.

Worked Example and Where SOHCAHTOA Appears in Exams

Example: A right-angled triangle has hypotenuse 10 cm and one angle 35°. Find the opposite side. Opposite and hypotenuse → use sin. sin 35° = opposite/10, so opposite = 10 × sin 35° ≈ 5.74 cm. Always label the triangle (O, A, H) for the angle you are using. SOHCAHTOA appears in trigonometry questions, bearings, angles of elevation and depression, and sometimes in geometry. Common errors: Using the wrong ratio; calculator in radians instead of degrees; rounding too early. Keep full accuracy until the final answer.

Tutopiya Resources and Free Trial

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