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
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.
Practice questions for Trigonometry (SOH CAH TOA)
Which trigonometric ratio connects the opposite side and the hypotenuse in a right-angled triangle?
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.