There are three tools at GCSE: right-angled trigonometry, the sine rule and the cosine rule. Deciding between them takes ten seconds if you look at the triangle before touching the calculator.
A decision rule that works
| What the triangle gives you | Use |
|---|---|
| A right angle | SOHCAHTOA (or Pythagoras if no angles are involved) |
| A matching side and opposite angle pair | Sine rule |
| Two sides and the angle between them | Cosine rule |
| Three sides, angle wanted | Cosine rule rearranged |
| Two sides and the included angle, area wanted | ½ab sin C |
Exact values you must know
Sine, cosine and tangent of 0°, 30°, 45°, 60° and 90° are required from memory on Higher tier and are needed for surd-form answers. Learn them as one small table and rewrite it from blank each morning during revision.
Bearings and 3D questions
Bearings are measured clockwise from north and written with three figures. In 3D problems, identify the right-angled triangle you are working in and redraw it flat on its own before doing any calculation — almost every 3D question reduces to two ordinary triangles.