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Sine and cosine rules

IGCSE Mathematics 0580, topics 6.5 and 6.6 (Extended). The sine rule, the cosine rule, area = ½ab sin C and the ambiguous case in any triangle, choosing the right rule, and Pythagoras and trigonometry in 3D.

About this lab: Sine and cosine rules

Interactive simulation for Cambridge IGCSE Mathematics 0580 topics 6.5 and 6.6: drag a triangle to see the sine rule ratios stay equal, the cosine rule turn into Pythagoras at 90° and grow for obtuse angles, area = ½ab sin C with its height, the ambiguous case with a side swinging like a compass to give two, one or no triangles, practice choosing the sine rule, cosine rule or area formula step by step, and the angle between a line and a plane in a cuboid and a square-based pyramid.

IGCSE Mathematics 0580, topics 6.5 and 6.6 (Extended). The sine rule, the cosine rule, area = ½ab sin C and the ambiguous case in any triangle, choosing the right rule, and Pythagoras and trigonometry in 3D.

Sine and cosine rules is a free, browser-based simulation for Cambridge IGCSE Mathematics 0580 (topic 6 Trigonometry, sections 6.5 Non-right-angled triangles (Extended), 6.6 Pythagoras' theorem and trigonometry in 3D (Extended)). The course is assessed in Paper 1 (Core non-calculator), Paper 2 (Extended non-calculator), Paper 3 (Core calculator), Paper 4 (Extended calculator). Syllabus for examination in 2025-2027. There are 6 tabs, each a self-contained experiment with its own controls and live readings, and nothing to install: it runs on a laptop, tablet or classroom projector.

Syllabus coverage

Full syllabus map: IGCSE Mathematics 0580 topic 6.

How to use this simulation

  1. 1. Sine rule.
  2. 2. Cosine rule.
  3. 3. Area ½ab sin C.
  4. 4. Ambiguous case.
  5. 5. Which rule?
  6. 6. 3D problems.
  7. The buttons at the end of the tab strip give the scene the whole window (Full screen, Hide controls) and, on a dark stage, a projector-friendly palette (Light scene). Many scenes also have drag handles: drag them to change the set-up directly.

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