TRIGONOMETRY Zambak
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zambak
Ahmet Chakir
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TRIGONOMETRY Zambak
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68
1. Introduction to Trigonometry
Theory
Page 10
1A. Angles and the Unit Circle
Theory
Page 10
1B. Basic Trigonometric Ratios
Theory
Page 13
1C. Trigonometric Identities
Theory
Page 15
1D. Trigonometric Theorems
Theory
Page 17
1D1. Basic Theorems
Theory
Page 17
1D2. Formulas for the Area of a Triangle
Theory
Page 18
1E. Trigonometric Formulas
Theory
Page 19
1E1. Sum and Difference Formulas
Theory
Page 19
1E2. Double-Angle and Half-Angle Formulas
Theory
Page 20
1E3. Reduction Formulas
Theory
Page 22
1E4. Sum to Product Formulas
Theory
Page 24
1E5. Product to Sum Formulas
Theory
Page 25
Applications of Trigonometry
Theory
Page 26
Exercises 1
Problem
Page 28
2. Trigonometric Functions
Theory
Page 30
2A. Trigonometric Functions and Their Properties
Theory
Page 30
2A1. The Sine Function
Theory
Page 30
2A2. The Cosine Function
Theory
Page 31
2A3. The Tangent Function
Theory
Page 33
2A4. The Cotangent Function
Theory
Page 34
2A5. The Secant Function
Theory
Page 35
2A6. The Cosecant Function
Theory
Page 36
2A7. Mixed Examples
Theory
Page 36
2B. Periods of Trigonometric Functions
Theory
Page 40
2B1. Periodic Functions
Theory
Page 40
2B2. Periods of Trigonometric Functions
Theory
Page 42
2C. Graphs of Trigonometric Functions
Theory
Page 46
2C1. Graph of the Sine Function
Theory
Page 46
2C2. Graph of the Cosine Function
Theory
Page 47
2C3. Graph of the Tangent Function
Theory
Page 48
2C4. Graph of the Cotangent Function
Theory
Page 48
2C5. Graph of the Secant Function
Theory
Page 49
2C6. Graph of the Cosecant Function
Theory
Page 50
2C7. Graph Translations
Theory
Page 50
2D. Inverse Trigonometric Functions
Theory
Page 54
2D1. The Arcsine Function
Theory
Page 55
2D2. The Arccosine Function
Theory
Page 57
2D3. The Arctangent Function
Theory
Page 60
2D4. The Arccotangent Function
Theory
Page 61
Mathematics and Music
Theory
Page 64
Exercises 2
Problem
Page 66
3. Trigonometric Equations and Inequalities
Theory
Page 71
3A. Types of Trigonometric Equation
Theory
Page 71
3A1. Basic Equations
Theory
Page 71
3A2. Factorizing Equations
Theory
Page 78
3A3. Equations with a Common Ratio
Theory
Page 84
3A4. Linear Equations in sin x and cos x
Theory
Page 87
3A5. Homogeneous Equations in sin x and cos x
Theory
Page 90
3A6. Maximum and Minimum Values of a Trigonometric Function
Theory
Page 92
3B. Further Trigonometric Equations
Theory
Page 95
3B1. Trigonometric Equations with an Absolute Value
Theory
Page 95
3B2. Parametric Equations
Theory
Page 96
3B3. Equations with Inverse Trigonometric Functions
Theory
Page 97
3B4. Systems of Trigonometric Equations
Theory
Page 97
3B5. Mixed Examples
Theory
Page 99
3C. Trigonometric Inequalities
Theory
Page 102
3C1. Basic Trigonometric Inequalities
Theory
Page 102
3C2. Advanced Trigonometric Inequalities
Theory
Page 112
Abul Wafa Buzjani and Nasir al-Din al Tusi
Other
Page 118
Exercises 3
Problem
Page 120
Chapter Summary
Theory
Page 124
Concept Check
Test
Page 131
Chapter Review Test 1
Test
Page 132
Chapter Review Test 2
Test
Page 134
Chapter Review Test 3
Test
Page 136
Answers
Answer
Page 138
Glossary
Other
Page 143
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