# TRIGONOMETRY – ENGLISH – CHAPTERS

##### Introduction

Explanations about the scope of the contents covered in the course, as well as by the topics of each of its chapters.

##### Chapter 1

Basic Definitions
Scalar and Vector Quantities
Presentation of Direction
Vectors
Direction, Orientation and Module
Types of Vectors
Geometric Sum of Vectors
Result of the Geometric Sum of Two Vectors
Theorem of Chasles
Point and Vector Projections
Theorem of Carnot
Problems to be Solved

##### Chapter 2

Circumference
Oriented Circumference
Orientation and Dimension of Arcs
Dimension of Total Arc of Circumference
Multiple Dimension of the Same Arc
Multiple Dimension of the same Angle
Trigonometry – Definitions
Trigonometric Circumference
Problems to be Solved

##### Chapter 3

Definition, Behavior, Behavior Graph of Functions
Sine
Cosine
Tangent
Cotangent
Secant
Cosecant
Problems to be Solved

##### Chapter 4

Fundamental or Basic Relations between Trigonometric Functions
Development of Basic Relationships between Functions
Derived Relationships between Functions
Problems to be Solved

##### Chapter 5

Relations between Arcs
Values of Functions for Symmetric Arcs
Values of Functions for Complementary Angles
Values of Functions for Supplementary Angles
Value of Functions for Angles that differ by 180
Reduction of any Angle to an Angle of First Quadrant
Problems to be Solved

##### Chapter 6

Expressions for Addition and Subtraction of Angles
Algebraic Value of the Vector Projected on an Axis
Algebraic Expressions for Sums of Two Angles
Algebraic Expressions for Sums of Three Angles
Algebraic Expressions for Subtraction of Two Angles
Algebraic Expressions for Multiple Angles
Algebraic Expressions for Functions of Half Angle
Algebraic Expressions for Functions with Full Angle referenced to Functions of Half Angles
Conversion of Expressions Type Addiction and Subtraction in Expressions Type Product and Vice Versa
Problems to be Solved

##### Chapter 7

Table of Values of Trigonometric Functions
Function Value for 0 Degrees
Function Value for 90 Degrees
Function Value for 45 Degrees
Function Value for 60 Degrees
Function Value for 30 Degrees
Function Value for 15 Degrees
Function Value for 75 Degrees
Trigonometric Circumference
Table with Values of the Trigonometric Functions
Problems to be Solved

##### Chapter 8

Solutions of Trigonometric Equations
Sequence for the Solution of Trigonometric Equations
10 Solved Problems
17 Problems to be Solved

##### Chapter 9

Resolution of Triangles using Trigonometry
Relationship between Elements of a Right Triangle
Solutions for Right Triangles,
Cases for Right Triangles
Solutions for any Triangle
Theorem or Law of Sines
Theorem or Law of Cosines
Cases for Any Triangle
Area of Any Type of Triangle
Topics of Basic Geometry
36 Problems to be Solved