Topic summary · Pure intermediate (P2)

Trigonometry summary

A-level trigonometry covers identities, equations and graphs beyond right-angled triangle ratios.

Open Learning Sheet — Trigonometry Download Trigonometry answers PDF

Files: P2-Trigonometry.pdf · P2-Trigonometry answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

$\sin^2\theta+\cos^2\theta=1$ and related $\tan$ identities.
Solve by rearranging to one trig function, then list all solutions in the interval.
Exact values for key angles are examinable.
Use CAST or a sketch to find companion solutions.

Worked example 1 — Find a side

Opposite $x$ , hypotenuse $10$ , angle $30^\circ$ . Find $x$ .

Working

x=10\sin30=5

SOH.

Worked example 2 — Find an angle

Adjacent $4$ , hypotenuse $8$ . Find $\theta$ .

Working

\cos\theta=\tfrac{1}{2}\Rightarrow\theta=60^\circ

CAH.

Worked example 3 — Tangent

Opposite $3$ , adjacent $3$ . Find $\theta$ .

Working

\tan\theta=1\Rightarrow\theta=45^\circ

TOA.

Worked example 4 — Equation

Solve $\sin\theta=\frac{1}{2}$ for $0^\circ\le\theta\le 360^\circ$ .

Working

\theta=30^\circ,\ 150^\circ

Sine is positive in the first and second quadrants.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning Sheet Answers PDF

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