Trigonometry Reciprocal Trigonometry Functions Connections to the Study
- Slides: 34
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 •