Study Notes
Trigonometric ratios are used to solve problems involving triangles and to understand the properties of trigonometric functions. They include the cosine rule, sine rule, and the properties of trigonometric graphs.
- Cosine Rule — Used to find a missing side or angle in a triangle when certain sides and angles are known. Example: To find an unknown side given two sides and the angle between them, use the cosine rule.
- Sine Rule — Used to find a missing side or angle in a triangle when certain sides and angles are known. Example: To find an unknown angle given two sides and one opposite angle, use the sine rule.
- Area of a Triangle — Formula to find the area when two sides and the angle between them are known. Example: Area = ½ab sin C.
- Graphs of Trigonometric Functions — Sine, cosine, and tangent graphs are periodic and have specific properties like amplitude and period. Example: The graph of y = sin θ has a period of 2π and an amplitude of 1.
- Transforming Trigonometric Graphs — Trigonometric graphs can be transformed using translations and stretches. Example: y = f(x) + a translates the graph vertically by a units.
Exam Tips
Key Definitions to Remember
- Cosine Rule: Used to find missing sides or angles in triangles.
- Sine Rule: Used to find missing sides or angles in triangles.
- Period: The interval at which a trigonometric graph repeats.
- Amplitude: Half the distance between the maximum and minimum points of a graph.
Common Confusions
- Confusing the sine and cosine rules when solving triangle problems.
- Misinterpreting the period and amplitude of trigonometric graphs.
Typical Exam Questions
- How do you find a missing side using the cosine rule? Use the formula c² = a² + b² - 2ab cos(C).
- How do you find an angle using the sine rule? Use the formula sin(A)/a = sin(B)/b.
- What is the period of the sine function? The period is 2π.
What Examiners Usually Test
- Ability to apply the sine and cosine rules in solving triangle problems.
- Understanding of the properties of trigonometric graphs, including period and amplitude.
- Skill in transforming trigonometric graphs using translations and stretches.