Summary
Trigonometry involves the study of angles and the relationships between the sides of triangles. It includes understanding trigonometric ratios, angles, and their properties on the Cartesian plane.
- Trigonometric Ratios — relationships between the angles and sides of a right triangle. Example: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent.
- General Angle Definition — angles measured from the positive x-axis, with anticlockwise as positive and clockwise as negative. Example: An angle in the second quadrant is between 90° and 180°.
- Trigonometric Graphs — graphical representations of sine, cosine, and tangent functions. Example: The sine graph repeats every 2π and has an amplitude of 1.
- Trigonometric Identities — equations true for all values of the variable involved. Example: sin²(θ) + cos²(θ) ≡ 1.
Exam Tips
Key Definitions to Remember
- Trigonometric Ratios: sin(θ), cos(θ), tan(θ)
- General Angle: Measured from the positive x-axis
- Trigonometric Identities: Equations true for all variable values
Common Confusions
- Mixing up sine and cosine graphs
- Forgetting the sign changes in different quadrants
Typical Exam Questions
- What is sin(45°)? Answer: √2/2
- How do you find the angle in the third quadrant with a basic angle of 30°? Answer: 180° + 30° = 210°
- What is the period of the sine function? Answer: 2π
What Examiners Usually Test
- Understanding and application of trigonometric ratios
- Ability to solve trigonometric equations
- Knowledge of graph transformations and properties