Trigonometry
The study of triangles — measuring the world through angles and sides, from right-angled pyramids to navigation across oceans.
اقرأ هذا الدرس مشروحاً بالعربي ←
The Big Picture
You can calculate perimeters, areas, and volumes. Now let us discover how angles and sides are linked by ratios — a tool that unlocks distances you cannot measure directly.
Imagine standing on one side of a canyon, wanting to know how wide it is without crossing. Trigonometry is that superpower. We start with the famous Pythagoras theorem for right triangles, then unlock sine, cosine, and tangent.
Formula
We'll go beyond right angles to solve any triangle, and finally step into three dimensions — because the real world isn't flat.
Memory trick
SOH CAH TOA is your secret password to unlock any right triangle in the universe.
What You Will Learn
You will start with right-angled triangles, where the three ratios do all the work, then move to triangles with no right angle, and finish inside solid shapes.
Steps
- 1
Labelling a right-angled triangle, and the tangent, sine and cosine ratios.
- 2
Pythagoras' theorem, and using it together with trigonometry.
- 3
Bearings and back bearings, and angles of elevation and depression.
- 4
Exact ratios for the special angles, and the sine and cosine graphs.
- 5
The sine rule and its ambiguous case, the cosine rule, and area using sine.
- 6
Three dimensions: cuboids, pyramids, and the angle between a line and a plane.
Formula
When there is no right angle, reach for the cosine rule:
It finds a missing side from two sides and the angle between them.
Practise trigonometry now
Interactive visual aids, then real past-paper questions marked on your working like the exam. Free to start.
Practise free on LemmaraLemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education or Pearson Edexcel. The lessons and worked examples are Lemmara’s own.