It is not for nothing that mathematics is considered the queen of sciences, because it is the most accurate of all the existing ones. This is a fundamental science that helps to find and explain the general laws of nature. One of the branches of mathematics is trigonometry.
Trigonometry Overview
Trigonometry is a field of mathematical knowledge that specializes in the study of trigonometric functions that are used in geometry.
The history of trigonometric functions is associated with a certain stage in the development of science and human achievements. Trigonometry arose at a time when architecture, science, and crafts already existed in the world. The beginnings of trigonometry loomed on the horizon of scientific knowledge at the moment when people began to intensively study rectangular triangles and trace the regular relationship between the lengths of the sides at sharp angles and the sharpest corners themselves.
If we turn to history, we can say that it was the ancient Greek mathematicians, who set out to measure the length of the circle, realized that this can be done by first measuring the length of the arc (25% of the entire length of the circle), using the chord technique.
The first trigonometric tables were created by the ancient Greek mathematician Hipparchus of Nicaea, who was the first in the history of mankind to reduce the values of arcs and chords into tables for a set of different angles.
Trigonometric knowledge is used today in almost all sciences and branches of exact knowledge, which is a phenomenal fact. This knowledge is quite actively applied in physics, geometry, engineering, as well as in astronomy, geography, music, financial analysis, electronics, statistics, probability theory, medicine, pharmaceuticals, architecture and computer graphics.
Trigonometric functions
A set of trigonometric functions can be represented by the following classification:
- Direct functions - sine (sin x); cosine (cos x).
- Derived functions - tangent (tg x); cotangent (ctg x).
- Other functions - secant (sec x); cosecance (cosec x).
These functions are interconnected. Their practical application is regulated by several basic formulas, the remaining computational processes are accomplished by finding derivatives of these formulas.
Basic trigonometry formulas
Sine and cosine are functions that are graphically represented in the form of curves in the Cartesian coordinate system, known since school time (another name for this system is XU-area). The main properties of the curves are periodicity, infinite differentiation, continuity.
What to do if you urgently need to remember the 10th grade and the basic formulas of trigonometry? But there are no textbooks on algebra and geometry ... The table in which the basic formulas of trigonometry are given will help you.
This table is a good aid to remember what was studied back in high school. The table "Basic formulas of trigonometry" seems very complicated, because a lot of information is presented here, it seems that it is impossible to remember. But this is only at first glance. After all, there are only a few basic formulas, they are quite simple, and you can repulse from them and solve more difficult trigonometric problems. These basic formulas involve simple computational steps such as addition, division, multiplication, and subtraction.
What can trigonometry give to a person?
Today trigonometry is part of a specific harmonic analysis in mathematics, which the great minds of our time regularly study and try to perfect. Trigonometry is based on the specific functions of the mathematical apparatus, which is directly related to the study of vibrational movements and regularly recurring processes. These are, for example, periodic oscillations, waves, and even some atmospheric processes.