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LearnCambridge97092026–2027Paper 3 · Pure Mathematics 3Trigonometry

Paper 3 · Module

Trigonometry

4 subtopics≈ 175 min in total

Start the module: Reciprocal functions and their identities Open graphing calculator

Reciprocal functions and their identities
Three new functions that are just $1$ over the old ones: their values, their graphs with asymptotes, the two Pythagorean identities they satisfy, and how to use them to solve equations.
≈ 40 min
Compound-angle formulae
$\sin(A+B)$ is not $\sin A+\sin B$ . The correct formulae for $\sin(A\pm B)$ , $\cos(A\pm B)$ and $\tan(A\pm B)$ , how to use them for exact values, and how they turn awkward equations into $\tan\theta=k$ .
≈ 45 min
Double-angle formulae
Setting $B=A$ in the compound-angle formulae gives formulae for $\sin2A$ , $\cos2A$ and $\tan2A$ . Three versions of $\cos2A$ let you match the function in an equation, and they are essential for integration later.
≈ 45 min
The R-form (harmonic form)
Any combination $a\sin\theta+b\cos\theta$ is a single sine wave in disguise: $R\sin(\theta+\alpha)$ . How to find $R$ and $\alpha$ , and how this makes equations and maximum and minimum questions easy.
≈ 45 min