Page 2: Advanced Trigonometric Rules

This page delves into the sine and cosine rules for solving non-right triangles, along with applications in finding areas and arc lengths.

Definition: The sine rule states that a/sin A = b/sin B = c/sin C for any triangle

Example: Area of a triangle can be calculated using the formula Area = ½ab sin C

Highlight: The cosine rule (a² = b² + c² - 2bc cos A) is used when you know three sides (SSS) or two sides and the included angle (SAS)

Vocabulary: Radian measure is an alternative to degrees, where 2π radians equals 360°

Page 3: Compound Angle Formulas

This page covers compound angle formulas and their applications in solving trigonometric equations.

Definition: sin$A+B$ = sin A cos B + cos A sin B is a fundamental compound angle formula

Example: Double angle formulas like sin 2θ = 2sin θ cos θ are derived from compound angle formulas

Highlight: Factor formulas help simplify expressions involving sums and differences of trigonometric functions

Vocabulary: Double angle formulas are special cases of compound angle formulas where both angles are equal

Page 4: Advanced Applications

This page focuses on advanced applications including r cos(θ±α) and r sin(θ±α) expressions and small angle approximations.

Definition: Small angle approximations are useful simplifications when θ is close to zero: sin θ ≈ θ, cos θ ≈ 1 - θ²/2

Example: Converting √3sin θ - cos θ to r sin$θ-α$ form requires using compound angle formulas

Highlight: Maximum and minimum values of trigonometric expressions can be found using these transformations

Vocabulary: The amplitude $r$ represents the maximum displacement from the midline of a trigonometric function

Page 1: Basic Trigonometry Foundations

This page introduces fundamental trigonometric concepts and special angle values. The content covers basic trigonometric ratios, graphs, and identities.

Definition: The Pythagorean identity states that sin²θ + cos²θ = 1 for any angle θ.

Example: For a 45° angle, sin 45° = cos 45° = 1/√2, and tan 45° = 1

Highlight: The reciprocal trigonometric functions are derived from the basic ratios: secθ = 1/cosθ, cosecθ = 1/sinθ, and cotθ = 1/tanθ

Vocabulary: Special angles refer to commonly used angles (30°, 45°, 60°) with exact trigonometric values