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LearnCambridge97092026–2027Paper 1 · Pure Mathematics 1Trigonometry

Paper 1 · Module

Trigonometry

5 subtopics≈ 215 min in total

Start the module: Exact values and the unit circle Open graphing calculator

Exact values and the unit circle
How sine, cosine and tangent are defined for any angle using the unit circle, the CAST rule for signs, and the exact values at $30^\circ$ , $45^\circ$ and $60^\circ$ that you need without a calculator.
≈ 40 min
Graphs and transformations
The shapes of $y=\sin x$ , $y=\cos x$ and $y=\tan x$ , their symmetries, and how $a$ , $b$ , $c$ and $d$ in $y=a\sin(b(x-c))+d$ stretch and shift them. Then use the graphs to count solutions and model things that repeat.
≈ 45 min
Inverse trigonometric functions
Why $\sin x=\tfrac12$ has infinitely many solutions but $\sin^{-1}\tfrac12$ has only one, the restricted domains that make sine, cosine and tangent one-to-one, and the principal values your calculator gives.
≈ 35 min
Trigonometric identities
The two identities at the heart of AS trigonometry, where they come from, and how to use them to simplify expressions, find exact values and write clear proofs.
≈ 40 min
Solving trigonometric equations
How to find every solution of a trig equation in an interval: principal value, symmetry, and period. Then equations with $2x$ or $x+30^\circ$ inside, quadratics in $\sin x$ or $\cos x$ , and equations that need an identity first.
≈ 55 min