Cambridge IGCSE·Mathematics 0580·Extended Trigonometry In 3D

📋Key knowledge — Trigonometry

Formulas & equations

sin θ = opposite ÷ hypotenuse (SOHCAHTOA)
cos θ = adjacent ÷ hypotenuse
tan θ = opposite ÷ adjacent
Sine rule: a/sin A = b/sin B = c/sin C
Cosine rule: a² = b² + c² − 2bc cos A
Area of triangle = ½ ab sin C
Exact values: sin 30°=½, cos 30°=√3/2, tan 30°=1/√3
Exact values: sin 45°=√2/2, cos 45°=√2/2, tan 45°=1
Exact 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 Extended

7 Cambridge IGCSE 0580 questions on trigonometry in 3d at the Extended tier — each with its full mark scheme. For the Core 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.