Trigonometry Laws

Trigonometry Laws

Trigonometry laws include six famous laws called sine of an angle or trigonometric functions. In the past, the values ​​of these laws were calculated for many angles and made a table for them, before the invention of the computer, which greatly facilitated the matter.

It became easy to know the properties of the trigonometric angles, and to obtain distances that were not known within the geometric shapes, through the following trigonometry laws

1. The sine of the angle is abbreviated as (Sin).
2. Cosine and abbreviated as (Cos).
3. The tangent of the angle is abbreviated as (tan).
4. The cotangent is abbreviated as cot.
5. The secant is abbreviated as sec.
6. The cosecant is abbreviated as (csc).

Uses of the laws of trigonometry

Trigonometry laws are used in a range of different sciences, including what is used to calculate the properties of angles and geometric distances in a one-dimensional or three-dimensional range, including the following:

1. astronomy.
2. Surveying and map making.
3. Military science, such as artillery range calculation.
4. Space sciences, and because it is three-dimensional, so it uses the laws of spherical trigonometry.

History of trigonometry

Trigonometry appeared in ancient civilizations , in particular the Egyptian, Babylonian, Hindu and Chinese civilizations, which had great knowledge of architecture, and the laws of trigonometry contributed greatly to the development of the architectural form of these civilizations.

Trigonometry laws in Egyptian civilization

An ancient Egyptian papyrus called the Rhind was discovered, containing 84 arithmetic problems in the branches of algebra and geometry, dating back to 1800 BC, and it also contained five mathematical problems regarding seked.

Careful analysis of the texts and forms contained in this papyrus reveals that the word seked means slope, which was the basis for building huge architectural projects, including the pyramids, and which was the basis for establishing trigonometry laws.

Math problem about the pyramid

Scientists discovered an arithmetic problem in the seked papyrus, through which the ancient Egyptians knew how to calculate the tangent of the angle between the base and the face of a triangle, or the so-called “run-to-rise” ratio, which is what is called the modern name of the slope And that was accurate.

It represents one of the basic laws of trigonometry, proving that the ancient Egyptians were familiar with the calculations within the triangle, which can be considered elementary trigonometry.

Classical trigonometry

The word trigonometry was used from the Greek trigonon, meaning triangle, until about the 16th century, and was used to calculate the values ​​of the missing parts of a triangle, or any geometric figure that can be divided into a group of triangles.

This type of calculation was considered classical trigonometry, which differs from engineering sciences as it is mainly concerned with qualitative relations, but it was considered one of the engineering sciences until they were separated, and they became separate branches at the beginning of the seventeenth century.

Modern trigonometry

The laws of trigonometry appeared in their modern form in Greece, and were expressed in purely geometric terms, by Hipparchus and that was in the year (120-190 BC). inside a circle, so any side of the triangle becomes the hypotenuse of the circle.

Since any straight line connecting two points on the curve of the circle is called a hypotenuse, and from here the missing values ​​of this triangle can be calculated, Hipparchus was interested in astronomy, and he got this idea from the imaginary triangle drawn by three stars in the sky of the globe.

Trigonometry in Europe

The Almagest of Ptolemy was the first European work of trigonometry (100-170 AD), when he lived in the Egyptian city of Alexandria, which was the intellectual center of the Hellenistic world.

Not much was known about Ptolemy , despite his numerous writings and various works. Ptolemy had works in various sciences, including mathematics, geography and optics, but the most famous of them remained the Almagest.

Almagest

It is a set of books on astronomy, consisting of 13 books, which was the basic picture of this science as the Earth was considered the center of the universe, until the emergence of the system of Nicolaus Copernicus who developed the heliocentric theory in the middle of the sixteenth century.

Ptolemy was trying to develop astronomy through the use of the laws of trigonometry and he developed a table for the values ​​of trigonometric functions, and his conception of the universe was the presence of the Earth in the middle and the sun revolving around it with five planets, a number that was discovered at that time.

Trigonometry in India and the Islamic World

The following effective contributions to trigonometry came from India, and the sexagesimal system was used, through which scholars came to the decimal system , and when applied to Ptolemy's table, the laws of sine appeared in their modern form.

These contributions were transmitted to the Islamic world, while Europe was languishing in a period of darkness in the Middle Ages, Muslims transmitted this knowledge to them through their presence in Spain (Andalusia), Iraq and Persia, which was the beginnings of the emergence of the calculator.

Spherical trigonometry

As a result of the dominance of astronomy over the natural sciences, until the sixteenth century, it was spherical trigonometry that scientists are interested in, and there are many differences between flat and spherical triangles, including

1. The two spherical triangles are identical in size as well as in shape, but are similar only in the plane case.
2. The sum of the angles of a spherical triangle is always greater than 180 degrees, and the angles in a plane triangle are 180 degrees.

spherical triangle term

The term spherical triangle first appears in Book No. 1 of Sphaerica, which consists of three books by Menelaus in the Egyptian city of Alexandria in AD 100, where he developed spherical mathematical equations for Euclid's representations of planar triangles.

A spherical triangle has been described as meaning a geometric figure, consisting of three arcs, of the large circles on the surface of a sphere, and these circles coincide with the center of the sphere, so it differs from the planar triangle in laws and angle values.

The laws of trigonometry contributed greatly to the modern scientific development, which science has reached now, as it was the reason for the existence of the wonderful architectural arts in ancient times, and the knowledge of astronomy and the discovery of the universe began with it. The other, and showed the virtue of ancient civilizations over our modern world.