Topic summary · Foundation · CIE Core

Trigonometry summary

Right-angled trigonometry uses $\sin$ , $\cos$ , $\tan$ with opposite, adjacent and hypotenuse. Label the triangle before choosing a ratio.

Open Learning Sheet — Trigonometry Download Trigonometry answers PDF

Files: foundation-31 Trigonometry handout.pdf · foundation-31 Trigonometry handout answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

SOH-CAH-TOA: pick the ratio that uses the sides you know/need.
To find an angle, use the inverse function.
Check your calculator is in degrees for IGCSE questions.

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.

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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