Exercises of Goniometry 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:
goniometric functions and properties
remarkable formulas
goniometric equations and inequalities.
Initial theoretical hints are also presented to make the performance of the exercises understood

Leseprobe

Table of Contents

"Exercises of Goniometry"

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

"Exercises of Goniometry"

SIMONE MALACRIDA

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

goniometric functions and properties

remarkable formulas

goniometric equations and inequalities.

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

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II – EXERCISES

Exercise 1 _

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

Exercise 18

Exercise 19

INTRODUCTION

In this exercise book some examples of calculations relating to the trigonometric functions are carried out.

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.

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

Angles are measured in degrees and the sexagesimal numbering system is applied to them which tends to divide a degree into 60 minutes and a first into 60 seconds.

A round angle corresponds to 360°, a flat angle to 180°, a right angle to 90°.

An obtuse angle is between 90° and 180°, an acute angle is less than 90°.

In goniometry we tend to use the notation in radians.

Radian is defined as the angle for which the subtended arc is equal to the radius of the circle.

To go from degrees to radians, just remember that a round angle is given by radians.

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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 .