Study Notes
3D trigonometry involves applying trigonometric skills to three-dimensional shapes to find missing sides or angles. It requires understanding which rules and formulae to use for different angles and side lengths.
- 3D Trigonometry — application of trigonometric skills in 3D shapes Example: Calculating the length of a diagonal in a cuboid.
- Pythagoras’ Theorem — a formula to find the length of a side in a right-angled triangle Example: Using it to calculate the distance between two points in a cube.
- Angle Between a Line and a Plane — the angle formed between a line and a surface Example: Finding the angle between a diagonal and the base of a cuboid.
Exam Tips
Key Definitions to Remember
- 3D Trigonometry: Application of trigonometry in three dimensions
- Pythagoras’ Theorem: a² + b² = c² for right-angled triangles
- Angle Between a Line and a Plane: Angle formed between a line and a surface
Common Confusions
- Mixing up which trigonometric ratio to use
- Confusing the angle between a line and a plane with angles within the plane
Typical Exam Questions
- Calculate the length of a diagonal in a cuboid? Use Pythagoras’ theorem in 3D.
- Find the angle between a line and the base of a cuboid? Use trigonometric ratios.
- Determine the length of a side in a triangular prism? Apply Pythagoras’ theorem.
What Examiners Usually Test
- Ability to apply trigonometric ratios in 3D
- Use of Pythagoras’ theorem in three-dimensional problems
- Understanding of angles between lines and planes