Introduction to Goniometry and Trigonometry E-Book

Simone Malacrida

• Herausgeber: Simone Malacrida
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

The theoretical assumptions of the following mathematical topics are presented in this book:
goniometric functions
goniometric equations and inequalities
trigonometry
Each topic is treated by emphasizing practical applications and solving some significant exercises.

Leseprobe

Table of Contents

“Introduction to Goniometry and Trigonometry"

INTRODUCTION

GONIOMETRIC FUNCTIONS

TRIGONOMETRY

“Introduction to Goniometry and Trigonometry"

SIMONE MALACRIDA

The theoretical assumptions of the following mathematical topics are presented in this book:

goniometric functions

goniometric equations and inequalities

trigonometry

Each topic is treated by emphasizing practical applications and solving some significant exercises.

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Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – GONIOMETRIC FUNCTIONS

Definitions

Angle measurement

Properties of sine and cosine

Trigonometric tangent

Remarkable trigonometric formulas

Trigonometric equations and inequalities

Reciprocal trigonometric functions

Inverse trigonometric functions

Applications

Exercises

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II – TRIGONOMETRY

Definition

Theorems

Resolution of triangles

Exercises

INTRODUCTION

This book presents the trigonometric functions and applications concerning these functions, in particular trigonometry.

The introduction of trigonometric functions allows to solve many problems, above all the geometric relationships between triangles and circles.

The formalism of these functions is of fundamental importance for analytical geometry and for analysis.

Furthermore, they are peculiar to many physical phenomena, from the characterization of wave phenomena to mechanics.

Each of the two chapters will be accompanied by some final exercise. This manual is not a workbook and, precisely for this reason, you will not find hundreds of exercises.

The questions proposed were considered significant for understanding the main rules and for their application.

In addition, particular emphasis has been given to the method of solving them since the real leap in quality between the study of a rule and its application is given precisely by the method, i.e. by the quality of the reasoning, and not by the quantity of calculations.

The program presented in this manual coincides, broadly, with what is taught in technical institutes and high schools, generally in the fourth year.

I

GONIOMETRIC FUNCTIONS

Definitions

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In the Cartesian plane we consider the circumference of unit radius, also called the trigonometric circle.

Its equation is given by:

We identify the abscissa of the generic point B belonging to this circle.

The variation of this abscissa based on the subtended angle between the x-axis and the ray joining the origin to B is a function called cosine.

The same can be done with the ordinate of this point and the resulting function is called sine. Both functions take the angle as an argument and that is why they are called trigonometric .

All of this is summarized in the figure below.