Understand and use the definitions of sine, cosine and tangent for all arguments; the sine and cosine rules; the area of a triangle in the form \(\frac{1}{2}ab\sin{C}\).

Work with radian measure, including use for arc length and area of sector.

Trigonometric ratios Sine and cosine rules, area of a triangle Radians Arc length, area of a sector

Understand and use the standard small angle approximations of sine, cosine and tangent.

\(\sin{\theta}≈\theta\), \(\cos{\theta}≈1−\frac{\theta^2}{2}\), \(\tan{\theta}≈\theta\) where \(\theta\) is in radians.

Small angle approximations

Understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity.

Know and use exact values of \(\sin\) and \(\cos\) for \(0\), \(\frac{π}{6}\), \(\frac{π}{4}\), \(\frac{π}{3}\), \(\frac{π}{2}\), \(\pi\) and multiples thereof, and exact values of \(\tan\) for \(0\), \(\frac{π}{6}\), \(\frac{π}{4}\), \(\frac{π}{3}\), \(\pi\) and multiples thereof.

Trigonometric graphs, exact values

Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; their relationships to sine, cosine and tangent; understanding of their graphs; their ranges and domains.

Reciprocal trigonometric functions Inverse trigonometric functions

Understand and use \(\tan{\theta}≡\frac{\sin{\theta}}{\cos{\theta}}\).

Understand and use \(\sin^2{\theta} + \cos^2{\theta} ≡ 1\); \(\sec^2{\theta} ≡ 1 + \tan^2{\theta}\) and \(\cosec^2{\theta} ≡ 1 + \cot^2{\theta}\).

Trigonometric identities

Understand and use double angle formulae; use of formulae for \(\sin{(A±B)}\), \(\cos{(A±B)}\) and \(\tan{(A±B)}\); understand geometrical proofs of these formulae.

Understand and use expressions for \(a\cos{\theta} + b\sin{\theta}\) in the equivalent forms of \(r\cos{(\theta±\alpha)}\) or \(r\sin{(\theta±\alpha)}\).

Addition and double angle formulae a cosθ + b sinθ

Solve simple trigonometric equations in a given interval, including quadratic equations in \(\sin\), \(\cos\) and \(\tan\) and equations involving multiples of the unknown angle.

Solve trigonometric equations

Construct proofs involving trigonometric functions and identities.

Proofs involving trigonometry

Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces.

Solve problems using trigonometry