A-level Mathematics₇₃₅₇

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 $\frac{\mathsf{1}}{\mathsf{2}}\mathit{a}\mathit{b}\mathsf{sin}\mathsf{}\mathit{C}$

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

$\mathsf{sin}\mathsf{}\mathit{\theta }\mathsf{\approx }\mathit{\theta }\mathsf{,}\mathit{ }\mathsf{cos}\mathsf{}\mathit{\theta }\mathsf{\approx }\mathsf{1}\mathsf{-}\frac{{\mathit{\theta }}^{\mathsf{2}}}{\mathsf{2}}\mathsf{,}\mathit{ }\mathsf{tan}\mathsf{}\mathit{\theta }\mathsf{\approx }\mathit{\theta }$ where $\mathit{\theta }$ 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 $\mathsf{0}\mathsf{,}\mathit{ }\frac{\mathsf{\pi }}{\mathsf{6}}\mathsf{,}\frac{\mathsf{\pi }}{\mathsf{4}}\mathsf{,}\frac{\mathsf{\pi }}{\mathsf{3}}\mathsf{,}\frac{\mathsf{\pi }}{\mathsf{2}}\mathsf{,}\mathit{ }\mathsf{\pi }$ and multiples thereof, and exact values of tan for $\mathsf{0}\mathsf{,}\mathit{ }\frac{\mathsf{\pi }}{\mathsf{6}}\mathsf{,}\frac{\mathsf{\pi }}{\mathsf{4}}\mathsf{,}\frac{\mathsf{\pi }}{\mathsf{3}}\mathsf{,}\mathsf{\pi }$ 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 $\mathsf{tan}\mathsf{}\mathit{\theta }\mathsf{\equiv }\frac{\mathsf{sin}\mathsf{}\mathit{\theta }}{\mathsf{cos}\mathsf{}\mathit{\theta }}$

Understand and use ${\mathsf{sin}}^{\mathsf{2}}\mathsf{}\mathit{\theta }\mathsf{+}{\mathsf{cos}}^{\mathsf{2}}\mathsf{}\mathit{\theta }\mathsf{\equiv }\mathsf{1}$ ; ${\mathsf{sec}}^{\mathsf{2}}\mathsf{}\mathit{\theta }\mathit{}\mathsf{\equiv }\mathsf{1}\mathit{}\mathsf{+}\mathit{}{\mathsf{tan}}^{\mathsf{2}}\mathsf{}\mathit{\theta }$ and ${\mathsf{cosec}}^{\mathsf{2}}\mathsf{}\mathit{\theta }\mathsf{\equiv }\mathsf{1}\mathsf{+}{\mathsf{cot}}^{\mathsf{2}}\mathsf{}\mathit{\theta }$

Understand and use double angle formulae; use of formulae for $\mathsf{sin}\mathsf{}\left(\mathit{A}\mathsf{\pm }\mathit{B}\right)\mathsf{,}\mathsf{cos}\mathsf{}\left(\mathit{A}\mathsf{\pm }\mathit{B}\right)\begin{array}{cc}& \\ & \end{array}\mathsf{a}\mathsf{n}\mathsf{d}\begin{array}{cc}& \\ & \end{array}\mathsf{t}\mathsf{a}\mathsf{n}\mathsf{}\mathsf{(}\mathit{A}\mathsf{\pm }\mathit{B}\mathsf{)}$ ; understand geometrical proofs of these formulae.

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

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.