A-Level Maths AQA 7357

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.

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.

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.

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.

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 $\cosec^2{\theta} ≡ 1 + \cot^2{\theta}$.

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 $r\sin{(\theta±\alpha)}$.

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

Construct proofs involving trigonometric functions and identities.

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