IB Maths: Geometry & Trigonometry Revision

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When does Pythagoras' theorem (a²+b²=c²) apply?

Geometry & Trigonometry is a core part of IB Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.

Key concepts

Sine rulea/sin A = b/sin B = c/sin C.

Cosine rulea^2 = b^2 + c^2 - 2bc cos A.

Triangle areaArea = ½ab sin C with included angle C.

Ambiguous caseSine rule may give two valid triangles.

SAS triangleTwo sides + included angle - use cosine rule.

ASA triangleTwo angles + a side - use sine rule.

Pythagorean identitysin^2 θ + cos^2 θ = 1.

Double angle sinsin 2θ = 2 sin θ cos θ.

Double angle coscos 2θ = cos^2 θ - sin^2 θ = 1 - 2sin^2 θ.

Double angle tantan 2θ = 2 tan θ / (1 - tan^2 θ).

R-forma sin θ + b cos θ = R sin(θ + α).

R and alphaR = √(a^2 + b^2), tan α = b/a.

RadianAngle where arc length equals the radius.

Conversionπ radians = 180°; multiply by π/180.

Learn Geometry & Trigonometry step by step

Free interactive mini-lessons: short screens, worked examples and quick checks. Pick your exam board to open its course map, then tap L on this topic:

IB Mathematics: Analysis & Approaches · HL IB Mathematics: Analysis & Approaches · SL IB Mathematics: Applications & Interpretation · HL IB Mathematics: Applications & Interpretation · SL

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.

Practise Geometry & Trigonometry — free games

Test yourself with these quick revision games for this topic:

▶ Two Truths, One Lie ▶ Reveal Race ▶ Connections Grid ▶ Falling Words ▶ Word Web

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Geometry & Trigonometry

Key concepts

Common mistakes to avoid

Practise Geometry & Trigonometry — free games

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