Exercise 1 — Cambridge IGCSE 0580 Nov 2024 Paper 13 Q9
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Cambridge IGCSE·Mathematics 0580·Core
Trigonometry In 3D
Key knowledge — Trigonometry
Formulas & equations
sin θ = opposite ÷ hypotenuse (SOHCAHTOA)cos θ = adjacent ÷ hypotenusetan θ = opposite ÷ adjacentSine rule: a/sin A = b/sin B = c/sin CCosine rule: a² = b² + c² − 2bc cos AArea of triangle = ½ ab sin CExact values: sin 30°=½, cos 30°=√3/2, tan 30°=1/√3Exact values: sin 45°=√2/2, cos 45°=√2/2, tan 45°=1Exact values: sin 60°=√3/2, cos 60°=½, tan 60°=√3
Key facts & rules
- SOHCAHTOA only works in right-angled triangles.
- Sine rule: use when you know 2 sides + opposite angle, or 2 angles + any side.
- Cosine rule: use when you know 3 sides (to find an angle), or 2 sides + included angle.
- Bearing: measured clockwise from North, always written as 3 digits (e.g. 045°).
- Angle of elevation: measured upward from horizontal. Angle of depression: measured downward from horizontal.
- For graphs: sin and cos have period 360°, amplitude 1. tan has period 180°.
IGCSE Trigonometry — Trigonometry in 3D Practice Core
1 Cambridge IGCSE 0580 questions on trigonometry in 3d at the Core tier — each with its full mark scheme. For the Extended tier on the same skill, click here.
How to approach trigonometry in 3d — open the study guide
Trigonometry in 3D on IGCSE 0580
Identify the right-angled triangle within the 3D shape. Use Pythagoras to find diagonal lengths, then apply sin/cos/tan for angles. Sketch the relevant 2D triangle extracted from the 3D figure.
Practice exercises