Summary
Trigonometry involves studying angles and the relationships between their sides and functions. It includes understanding trigonometric ratios, graphs, inverse functions, equations, and identities.
- Angle — A measure of rotation from a line segment about a point. Example: An angle in the second quadrant is between 90° and 180°.
- Trigonometric Ratios — Ratios of the sides of a right triangle relative to an angle. Example: sin(30°) = 1/2, cos(60°) = 1/2, tan(45°) = 1.
- Trigonometric Functions — Functions like sine, cosine, and tangent that relate angles to ratios. Example: The sine function has a period of 2π and an amplitude of 1.
- Inverse Trigonometric Functions — Functions that reverse trigonometric functions, restricted to specific domains. Example: sin⁻¹(x) is the inverse of sin(x).
- Trigonometric Identities — Equations true for all values of the variable. Example: sin²θ + cos²θ ≡ 1.
Exam Tips
Key Definitions to Remember
- Trigonometric Ratios: sin, cos, tan
- Inverse Functions: sin⁻¹, cos⁻¹, tan⁻¹
- Trigonometric Identities: sin²θ + cos²θ ≡ 1
Common Confusions
- Mixing up the signs of trigonometric ratios in different quadrants
- Forgetting the period and amplitude of trigonometric functions
Typical Exam Questions
- What is the period of the sine function? 2π
- How do you find the angle in the third quadrant with a basic angle of 30°? θ = 180° + 30° = 210°
- What is the inverse of sin(x) when x = 1/2? sin⁻¹(1/2) = 30°
What Examiners Usually Test
- Ability to sketch and interpret graphs of trigonometric functions
- Solving trigonometric equations within specified intervals
- Understanding and applying trigonometric identities