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Topic summary · Foundation · CIE Core

Trigonometry summary

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

Open Learning Sheet — TrigonometryDownload 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 xx, hypotenuse 1010, angle 30∘30^\circ. Find xx.

xadjhypRight-angled triangle

Working

x=10sin⁡30=5x=10\sin30=5

SOH.

Worked example 2 — Find an angle

Adjacent 44, hypotenuse 88. Find θ\theta.

Working

cos⁡θ=12⇒θ=60∘\cos\theta=\tfrac{1}{2}\Rightarrow\theta=60^\circ

CAH.

Worked example 3 — Tangent

Opposite 33, adjacent 33. Find θ\theta.

Working

tan⁡θ=1⇒θ=45∘\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 SheetAnswers PDF
WorksheetsTopic summariesTopic videos
Trigonometry summary — worksheet & answers PDF