Trigonometry

Trigonometry on P1 goes well beyond right-angled triangles: non-right triangles, radians, graphs and equations all appear.

The sine and cosine rules

These work in any triangle (label sides $a, b, c$ opposite angles $A, B, C$).

Sine rule (a side and its opposite angle, plus one more): $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$
Cosine rule (two sides and the angle between, or all three sides): $a^2 = b^2 + c^2 - 2bc\cos A$
Area of a triangle: $\dfrac{1}{2}ab\sin C$ (two sides and the included angle)

Exam tip. Use the cosine rule when you know two sides and the angle between them (or three sides); use the sine rule otherwise. Watch for the "ambiguous case" where an obtuse angle is possible — the question often tells you the angle is obtuse.