A-Level Maths Specification

AQA 7357

Section E: Trigonometry

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#E1

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 12absinC\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

#E2

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

sinθθ\sin{\theta}≈\theta, cosθ1θ22\cos{\theta}≈1−\frac{\theta^2}{2}, tanθθ\tan{\theta}≈\theta where θ\theta is in radians.

Small angle approximations

#E3

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

Know and use exact values of sin\sin and cos\cos for 00, π6\frac{π}{6}, π4\frac{π}{4}, π3\frac{π}{3}, π2\frac{π}{2}, π\pi and multiples thereof, and exact values of tan\tan for 00, π6\frac{π}{6}, π4\frac{π}{4}, π3\frac{π}{3}, π\pi and multiples thereof.

Trigonometric graphs, exact values

#E4

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

#E5

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

Understand and use sin2θ+cos2θ1\sin^2{\theta} + \cos^2{\theta} ≡ 1; sec2θ1+tan2θ\sec^2{\theta} ≡ 1 + \tan^2{\theta} and cosec2θ1+cot2θ\cosec^2{\theta} ≡ 1 + \cot^2{\theta}.

Trigonometric identities

#E6

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

Understand and use expressions for acosθ+bsinθa\cos{\theta} + b\sin{\theta} in the equivalent forms of rcos(θ±α)r\cos{(\theta±\alpha)} or rsin(θ±α)r\sin{(\theta±\alpha)}.

Addition and double angle formulae a cosθ + b sinθ

#E7

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

Solve trigonometric equations

#E8

Construct proofs involving trigonometric functions and identities.

Proofs involving trigonometry

#E9

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

Solve problems using trigonometry