Chapter 9: Fundamentals of Trigonometry

9.1: Introduction

1. Meaning and Importance of Trigonometry
2. Problem 1: Meaning and Importance of Trigonometry

9.2: Units of Measures of Angles

1. Introduction to an Angle
2. Measuring an Angle in Sexagesimal System
3. Problem1-Measuring an Angle in Sexagesimal System
4. Sexagesimal System into Decimal form & Vice Versa
5. Problem-Sexagesimal System into Decimal form & Vice Versa
6. Radian Measure of an Angle
7. Problem-Radian Measure of an Angle
8. Problem2-Radian Measure of an Angle

9.3: Relation Between an Arc Length & Circular Measure of its Central Angle

1. Relationship of Radius-Central Angle-Arc Length
2. Problem 1: Relationship of Radius-Central Angle-Arc Length
3. Problem2-Relationship of Radius-Central Angle-Arc Length
4. Area of a Circular Sector.
5. Problem 1: Area of a Circular Sector.
6. Problem2-Area of a Circular Sector.
7. Problems Using Arcs and Sectors
8. More on Problems Using Arcs and Sectors
9. Relationship Between Radians & Degrees.

9.4: General Angle ( Coterminal Angles )

1. General Angles
2. Problem-General Angles

9.5: Angle in the Standard Position

1. Angle in Standard Position.
2. Problem-Angle in Standard Position
3. The Quadrants & Quadrantal Angles
4. Problem-The Quadrants & Quadrantal Angles

9.6: Trigonometric Functions

1. Trigonometric Ratios of an Acute Angle
2. Problem 1: Trigonometric Ratios of an Acute Angle
3. Trigonometric Ratios of an Complementary Angles
4. Problem 1: Trigonometric Ratios of an Complementary Angles

9.7: Trigonometric Functions of Any Angle

1. Trigonometric Ratios & Their Reciprocals
2. Problem1-Trigonometric Ratios & Their Reciprocals
3. Problem-Trigonometric Ratios & Their Reciprocals

9.8: Fundamental Identities

1. Proof of Fundamental Trigonometric Identity
2. More on Fundamental Trigonometric Identity
3. Problem 1: Proof of Fundamental Trigonometric Identity
4. Problem 2: More on Fundamental Trigonometric Identity
5. Problem 3: More on Fundamental Trigonometric Identity
6. Problem 4: More on Fundamental Trigonometric Identity
7. Problem5-Proof of Fundamental Trigonometric Identity
8. Problem 1: More on Fundamental Trigonometric Identity

9.9: Signs of the Trigonometric Functions

1. Signs of Trigonometric Ratios in Different Quadrants
2. Problem-Signs of Trigonometric Ratios in Different Quadrant
3. Problem2-Signs of Trigonometric Ratios in Different Quadrant
4. Trigonometric Functions for a Unit Circle

9.10: The Values of Trigonometric Functions of Acute Angles 45, 30 and 60 Degrees

1. Trigonometric ratios of 45 degree
2. Problem 1: Trigonometric ratios of 45 degree
3. Trigonometric ratios of 30 degree and 60 degree
4. Problem 1: Trigonometric ratios of 30 degree and 60 degree
5. Problem 2: Trigonometric ratios of 30 degree and 60 degree

9.11: The Values of the Trigonometric Functions of Angles 0, 90, 180, 270, 360 Degrees

1. Values of Trigonometric Ratios at Quadrantal Angle
2. Problem-Values of Trigonometric Ratios at Quadrantal Angle

9.12: Domains of Trigonometric Functions and of Fundamental Identities

1. Domain and Ranges of Trigonometric Functions and Fundamental Identiti
2. Problem1-Domain and Ranges of Trigonometric Functions and Fundamental
3. Problem2-Domain and Ranges of Trigonometric Functions and Fundamental
4. Problem3-Domain and Ranges of Trigonometric Functions and Fundamental