Fiducia TogetherTrigonometry
The relationships between angles and sides in triangles. SOHCAHTOA, and what to do when there is no right angle.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
Sine, cosine and tangent relate an angle in a right-angled triangle to ratios of its sides. SOHCAHTOA is the mnemonic: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
Where it applies
Both tiers for right-angled triangles. Higher adds the sine rule, the cosine rule and the area formula for non-right-angled triangles.
How it works
Label the sides relative to the ANGLE you are using — opposite and adjacent change when the angle changes.
For non-right-angled triangles: sine rule when you have a matching side-and-angle pair, cosine rule when you have three sides or two sides and the angle between them.
How to use it in your work
Check your calculator is in degrees. A calculator in radians produces answers that look plausible and are wrong.
Learn the exact values for 30°, 45° and 60° — Higher papers ask for exact answers where a calculator will not help.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.