Basics Of Trigonometric Functions

This section introduces the fundamental trigonometric functions and their relationships with right-angled triangles.

Definitions

This section outlines key definitions and fundamental concepts associated with trigonometric identities and functions essential for understanding geometry and trigonometry.

Right-Angled Triangle Definitions

This section introduces the fundamental definitions related to right-angled triangles in trigonometry, including the key trigonometric functions derived from these definitions.

Trigonometric Ratios In The Unit Circle

This section explores trigonometric ratios as defined by the unit circle, highlighting their relationships to angles and coordinates.

Unit Circle Properties

The section explains the unit circle's importance in trigonometry, detailing how trigonometric functions relate to angles on the circle.

Periodicity And Symmetry

This section explores the periodic nature and symmetry of trigonometric functions, focusing on the behaviors of sine and cosine functions.

Fundamental Trigonometric Identities

Fundamental trigonometric identities are critical equations involving trigonometric functions that hold true for all angles.

Pythagorean Identities

The Pythagorean identities are fundamental equations in trigonometry that relate the squares of sine, cosine, tangent, cotangent, secant, and cosecant.

Reciprocal Identities

Reciprocal identities relate the main trigonometric functions to their inverses.

Quotient Identities

Quotient identities define the relationships between the tangent and cotangent functions in terms of sine and cosine.

Co-Function And Negative Angle Identities

This section covers co-function identities and negative angle identities, crucial for understanding trigonometric functions and their relationships.

Trigonometric Graphs

This section covers the graphs of sine, cosine, and tangent functions, highlighting their shapes, key points, and characteristics such as amplitude and period.

Graph Of Y = Sin(Θ)

This section covers the key features and characteristics of the graph of the sine function, including its shape, amplitude, and period.

Graph Of Y = Cos(Θ)

This section discusses the graphical representation of the cosine function, its properties, and key evaluation points.

Graph Of Y = Tan(Θ)

This section focuses on the characteristics and behavior of the graph of the tangent function, y = tan(θ).

Transformations Of Trigonometric Graphs

This section covers how to analyze transformations of trigonometric graphs, focusing on changes to amplitude, period, phase shift, and vertical shift.

General Transformation Form

This section covers the general transformation form of trigonometric graphs, detailing how amplitude, period, phase, and vertical shifts modify the function.

Examples Of Transformations

This section delves into the transformations of trigonometric functions, illustrating how alterations in parameters affect the graphs.

Applications Of Trigonometric Graphs

This section focuses on the real-world applications of trigonometric graphs in various fields such as physics, engineering, and architecture.

Chapter Summary

This chapter covers trigonometric identities and graphs, vital for understanding the relationships between angles and sides of triangles and their applications.

Worked Examples

This section provides worked examples that illustrate the application of trigonometric identities and graph transformations in mathematics.

Example 1: Prove The Identity

Example 2: Graph Transformation

Practice Problems

This section presents practice problems to reinforce understanding of trigonometric identities and functions.