These are the statements describing what students need to learn:
- 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 ½absin(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
sinθ ≈ θ,
cosθ ≈ 1 - ½θ2
tanθ ≈ θ,
Where θ is in radians - understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity. Know and use exact values of sin, cos and tan for the following angles (in degrees and radians) 0°, 30°, 45°, 60°, 90°, 180° 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
tanθ = sinθ ÷ cosθ
sin2θ + cos2θ = 1
sec2θ = 1 + tan2θ and
cosec2θ = 1 + cot2θ - 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 cosθ + b sinθ in the equivalent forms of r cos (θ ± α) or r sin (θ ± α) - 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
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