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A-level Mathematics7357

7357

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3.6 E: Trigonometry

 
Content
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

12absin⁡C

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

 
Content
E2

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

sin⁡θ≈θ, cos⁡θ≈1-θ22, tan⁡θ≈θ
where
θ
is in radians.

 
Content
E3

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, π6,π4,π3,π2, π
and multiples thereof, and exact values of tan for
0, π6,π4,π3,π
and multiples thereof.

 
Content
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.

 
Content
E5

Understand and use

tan⁡θ≡sin⁡θcos⁡θ

Understand and use

sin2⁡θ+cos2⁡θ≡1
;
sec2⁡θ≡1+tan2⁡θ
and
cosec2⁡θ≡1+cot2⁡θ

 
Content
E6

Understand and use double angle formulae; use of formulae for

sin⁡A±B,cos⁡A±Bandtan⁡(A±B)
; understand geometrical proofs of these formulae.

Understand and use expressions for

acos⁡θ+bsin⁡θ
in the equivalent forms of
rcos⁡(θ±α)
or
rsin⁡(θ±α)

 
Content
E7

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

 
Content
E8

Construct proofs involving trigonometric functions and identities.

 
Content
E9

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