Geometry & MeasuresTopic Summary

Knowledge Organiser: Trigonometry — SOH CAH TOA

Part of Trigonometry (SOH CAH TOA) · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Trigonometry — SOH CAH TOA within Trigonometry (SOH CAH TOA) for GCSE Mathematics. Revise Trigonometry (SOH CAH TOA) in Geometry & Measures for GCSE Mathematics with 19 exam-style questions and 7 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 7 of 7

Practice

19 questions

Recall

7 flashcards

Knowledge Organiser: Trigonometry — SOH CAH TOA

Key Terms
  • Hypotenuse (H): Longest side, opposite the right angle
  • Opposite (O): Side opposite the angle you are working with
  • Adjacent (A): Side next to the angle (not the hypotenuse)
  • Inverse trig: sin⁻¹, cos⁻¹, tan⁻¹ — used to find angles
Must-Know Facts
  • Only works for RIGHT-ANGLED triangles
  • Label O, A, H from the angle you are working with — not from the right angle
  • Calculator MUST be in DEGREE mode (test: sin 30° = 0.5)
  • To find a side: rearrange the trig formula
  • To find an angle: use the inverse function (SHIFT + sin/cos/tan)
Key Formulas
  • SOH: sin θ = O ÷ H
  • CAH: cos θ = A ÷ H
  • TOA: tan θ = O ÷ A
  • Find side: O = H × sin θ, A = H × cos θ, O = A × tan θ
  • Find angle: θ = sin⁻¹(O/H), cos⁻¹(A/H), tan⁻¹(O/A)
Common Mistakes
  • Labelling sides from the wrong angle: O, A, H are always relative to the angle θ being used — relabel if the angle changes
  • Using sin when should use cos (or vice versa): Check which sides are known/needed — O&H → sin; A&H → cos; O&A → tan
  • Finding angle vs finding side: To find a side, multiply; to find an angle, use the inverse function (sin⁻¹ etc.)
  • Calculator in wrong mode: Always use DEGREE mode for GCSE — check the display shows D not R or G

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Keep building this topic

Read this section alongside the surrounding pages in Trigonometry (SOH CAH TOA). That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Trigonometry (SOH CAH TOA)

Which trigonometric ratio connects the opposite side and the hypotenuse in a right-angled triangle?

  • A. tan θ = opposite / adjacent
  • B. cos θ = opposite / hypotenuse
  • C. sin θ = opposite / hypotenuse
  • D. sin θ = adjacent / hypotenuse
1 markfoundation

For the triangle shown, a student chooses to use sin to find the missing side. Explain why they chose sin rather than one of the other trigonometric ratios.

2 marksstandard

Quick Recall Flashcards

SOH CAH TOA
Sin = O/H, Cos = A/H, Tan = O/A. Pick based on which two sides you have or need.
SOH CAH TOA
sin = Opp/Hyp, cos = Adj/Hyp, tan = Opp/Adj

19 questions on Trigonometry (SOH CAH TOA) — practise free

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