Trigonometry Reciprocal Trigonometry Functions Connections to the Study

Trigonometry

Reciprocal Trigonometry Functions Connections to the Study Design: AOS 1 – Functions and graphs • Graphs of the reciprocal circular functions cosecant, secant and cotangent, and simple transformations of these

Key Angle Vocabulary: Quadrant Functions CAST Unit Circle Equivalent Derive Reciprocal Relationship Abbreviate Magnitude Cosecant Radians Secant Compound- Cotangent Inverse Correspondi ng Rationalise Denominator Simplify Resulting •

Trig Recap •

Unit Circle - CAST

Exact Values in First Quadrant Angle (degree s) Angle (radian s) 0° 30° 45° 60° 90° 180° 270° 360° 0 sin(θ) 0 1 0 -1 0 cos(θ) 1 0 -1 0 Undefine d 0 tan(θ) 1

First Quadrant • •

Second Quadrant •

Third Quadrant •

Fourth Quadrant •

Summary •

Negative Angles • •

Reciprocal Trigonometric Functions Trigonometric Function • Sine Function • Cosine Function • Tangent Function • Note: these are not inverse trigonometric functions.

Exact Values Angles multiples of 30° and 45°: Exact values for reciprocal trigonometric functions can be found from corresponding trigonometric values.

Example 1: Exact Values •

Example 2: Using triangles to find values •

Trigonometric Identities using Reciprocal Trigonometric Functions •

Key Vocabulary: Cancelling Common Factors Identity Equation Denominators Mathematical Numerators Convention Prove Transform Fundamental Simplifying Relations Factorising Quotient •

Identities vs Equations •

Identities and Relations • •

Work Example 3: Identity Proof •

Work Example 4: Identity Proof •

Compound-angle Formulas •

Key Vocabulary: Corresponding Compound Theorems Perpendicular Expanding Properties Expressions Supplementary Complementary Substituting Multiples Derive Argument Ratio •

Summary of the compound-angle formulas •

Proof of the compound-angle formula: tangent

Worked Examples: Collaborative •

Double-angle formulas •

Key Vocabulary: Equivalent Common Factor Null Factor Law Reciprocal •

Double Angle Formulas •

Half-angle formulas •

Multiple-angle formulas •

Collaborative Work Examples •