Trigonometry & Pythagoras is a core part of GCSE Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.
Key concepts
SOHCAHTOAsin = opp/hyp, cos = adj/hyp, tan = opp/adj — for right-angled triangles.
Opposite, adjacent, hypotenuseSides labelled relative to a chosen angle (not the right angle).
Finding an angleUse inverse functions (sin⁻¹, cos⁻¹, tan⁻¹) on the ratio.
Exact valuessin 30° = 1/2, cos 60° = 1/2, tan 45° = 1; useful exact ratios.
Sine rulea / sin A = b / sin B = c / sin C — for any triangle.
Cosine rulea² = b² + c² − 2bc cos A — for any triangle when you have SAS or SSS.
Hypotenuse (H)Longest side, opposite the right angle.
Opposite (O)The side directly across from the chosen angle θ.
Adjacent (A)Side next to angle θ; not the hypotenuse.
SOHsin θ = Opposite ÷ Hypotenuse.
CAHcos θ = Adjacent ÷ Hypotenuse.
TOAtan θ = Opposite ÷ Adjacent.
Angle of elevationAngle measured up from horizontal to an object.
Angle of depressionAngle measured down from horizontal to an object.
Common mistakes to avoid
Questions where students often pick the tempting wrong answer — make sure you know the right one:
When does Pythagoras' theorem (a²+b²=c²) apply?✗ To any triangle. ✓ Only to right-angled triangles.
What do sin, cos and tan give you?✗ The angle directly. ✓ Ratios of sides — use inverse functions to find an angle.
In Pythagoras' theorem, which side does c^2 represent?✗ c^2 represents any side of the triangle as long as the other two are squared. ✓ The hypotenuse — the longest side, opposite the right angle.
Can Pythagoras' theorem be used on any triangle?✗ Yes — it works on any triangle as long as you square the sides. ✓ No — it only applies to right-angled triangles.
Does sin(2x) equal 2 sin(x)?✗ Sin is a function, so sin(2x) = 2 sin(x) by pulling the constant out. ✓ No — sin is not a linear function; sin(2x) = 2 sin(x) cos(x).
Practise Trigonometry & Pythagoras — free games
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