Exercises of Trigonometry E-Book

Simone Malacrida

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

Veröffentlichungsjahr: 2022

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics:
trigonometry applied to circumferences and triangles
solving right-angled triangles and any triangles
parametric trigonometric problems with discussion
Initial theoretical hints are also presented to make the performance of the exercises understood.

Leseprobe

Table of Contents

“Exercises of Trigonometry”

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

“Exercises of Trigonometry”

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

trigonometry applied to circumferences and triangles

solving right-angled triangles and any triangles

parametric trigonometric problems with discussion

Initial theoretical hints are also presented to make the performance of the exercises understood.

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 – THEORETICAL OUTLINE

Definition

theorems

Resolution of triangles

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II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercises or 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

INTRODUCTION

In this workbook, some examples of calculations related to trigonometry are done.

Trigonometry represents the main application of trigonometric functions and is the conceptual leap that distinguishes the study of modern plane geometry from what was done in antiquity (in particular by the Greeks).

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

What is exposed in this workbook is generally addressed during the fourth year of scientific high schools.

I

THEORETICAL OUTLINE

Definition

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Trigonometry applies trigonometric functions to geometry , in particular to triangles, generating new and broader results than those described when speaking of elementary geometry.

theorems

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The chord theorem states that, given a circumference and a generic chord AB, the ratio between the chord and the diameter is equal to the sine of any angle to the circumference that insists on the chord.

With reference to this figure:

The formula is as follows:

An application of the chord theorem is given by the theorem of sines .

Considering any triangle with sides equal to a,b,c, the ratio between each of the sides with the sines of the respective opposite angles is a constant equal to the diameter of the circumscribed circumference of the triangle.

The cosine (or Carnot) theorem generalizes the Pythagorean theorem for any triangle:

In fact, if the angle between b and c is right, we fall back on the well-known theorem already expressed.

We can also obtain a generalization for the area of any triangle: