# Trigonometry (study of triangles) in A-Level Maths

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## Trigonometry

**Trigonometry** is the study of triangles and many trigonometric functions come from studying triangles. You have seen some of these functions before. Namely the sin, cos and tan functions at GCSE. At A-Level, we study these and other trigonometric functions, their equations and also their identities. We also look at approximations in trigonometry as well as measuring angles and sketching curves using radians as opposed to degrees.

Firstly, basic trigonometric graphs, equations and identities are explored in the first year of A-Level Maths as well as non-right angled triangles. Then, in the second year, students will also look at radians, arcs & sectors, small angle approximations, the sec/cosec/cotan functions and inverse trigonometry.

## Other Areas in AS-Maths

- PROOF – proof by deduction, proof by exhaustion, disproof by counterexample
- ALGEBRA & FUNCTIONS – completing the square, cubics, curve sketching, discriminant, indices, inequalities, polynomials, quadratics, simultaneous equations, surds, transformations
- COORDINATE GEOMETRY – straight lines, equation of a circle
- SEQUENCES & SERIES – binomial expansion
- EXPONENTIALS & LOGS – exponential & logarithmic graphs, logs, their rules and solving log equations, growth & decay, differentiating e to the kx
- DIFFERENTIATION – differentiation from first principles and differentiating polynomials, increasing & decreasing functions, stationary points, tangents & normals, differentiating e to the kx
- INTEGRATION – fundamental theorem of calculus and integrating powers of x, definite integrals
- NUMERICAL METHODS – (not covered at AS Level)
- VECTORS – two-dimensional vectors, vector arithmetic, vectors in context

## Other Areas in A2-Maths

- PROOF – proof by contradiction
- ALGEBRA & FUNCTIONS – modulus of a function, partial fractions, inverse and composite functions, compound transformations
- COORDINATE GEOMETRY – parametric equations
- SEQUENCES & SERIES – arithmetic series (and sigma notation), geometric series, sequences, binomial expansion
- EXPONENTIALS & LOGARITHMS – compound transformations
- DIFFERENTIATION – concavity, convexity & inflection points, derivatives of trigonometric functions, product, quotient & chain rule, parametric & implicit differentiation, differentiating exp/log functions, differential equations & rates
- INTEGRATION – further integration, integration using trigonometric identities, integration by substitution, integration by parts, integration using partial fractions, solving differential equations,
- NUMERICAL METHODS – locating roots using iteration (including Newton-Raphson), trapezium rule
- VECTORS – 3D vectors