TRIGONOMETRY FUNCTIONS, EQUATIONS and INEQUALITIES
CHAPTER 1: INTRODUCTION TO TRIGONOMETRY
A. ANGLES AND THE UNIT CIRCLE
B. BASIC TRIGONOMETRIC RATIOS
C. TRIGONOMETRIC IDENTITIES
D. TRIGONOMETRIC THEOREMS
1. Basic Theorems
2. Formulas for the Area of a Triangle
E. TRIGONOMETRIC FORMULAS
1. Sum and Difference Formulas
-Shape(Figure) Examples Vid 1 ,
2. Double-Angle and Half-Angle Formulas
3. Reduction Formulas
4. Sum to Product Formulas
5. Product to Sum Formulas
Applications of Trigonometry
CHAPTER 2: TRIGONOMETRIC FUNCTIONS
A. TRIGONOMETRIC FUNCTIONS AND THEIR PROPERTIES
1. The Sine Function
2. The Cosine Function
3. The Tangent Function
4. The Cotangent Function
5. The Secant Function
6. The Cosecant Function
7. Mixed Examples
B. PERIODS OF TRIGONOMETRIC FUNCTIONS
1. Periodic Functions
2. Periods of Trigonometric Functions
C. GRAPHS OF TRIGONOMETRIC FUNCTIONS
1. Graph of the Sine Function
2. Graph of the Cosine Function
3. Graph of the Tangent Function
4. Graph of the Cotangent Function
5. Graph of the Secant Function
6. Graph of the Cosecant Function
7. Graph Translations
D. INVERSE TRIGONOMETRIC FUNCTIONS
1. The Arcsine Function
2. The Arccosine Function
3. The Arctangent Function
4. The Arccotangent Function
-Finding results of inverse trigonometric ratios Vid 1 ,
Mathematics and Music
CHAPTER 3: TRIGONOMETRIC EQUATIONS AND INEQUALITIES
A. TYPES OF TRIGONOMETRIC EQUATION
1. Basic Equations Vid 1 ,
2. Factorizing Equations
3. Equations with a Common Ratio
4. Linear Equations in sin x and cos x
5. Homogeneous Equations in sin x and cos x
6. Maximum and Minimum Values of a Trigonometric Function
B. FURTHER TRIGONOMETRIC EQUATIONS
1. Trigonometric Equations with an Absolute Value
2. Parametric Equations
3. Equations with Inverse Trigonometric Functions
4. Systems of Trigonometric Equations
5. Mixed Examples
C. TRIGONOMETRIC INEQUALITIES
1. Basic Trigonometric Inequalities Vid 1 , Vid 2 ,
2. Advanced Trigonometric Inequalities
Abul Wafa Buzjani and Nasir al-Din al Tusi