Trigonometry is the mathematical science of the trigonometric functions sin and cos. These relationships are basic concepts, without understanding them it will not be possible to study something new in this area. It's not difficult, the main thing is to understand where the values of cosines and sines come from and how to calculate them.
From the history of appearance
In the works of ancient Greek mathematicians already in the III century BC, there are ratios of segments of triangles. Menelaus explored them in ancient Rome. The mathematician Aryabhata from India also gave definitions to these concepts. He connected the calculations of the sine with "arkhajivs" (literal translation - half of the bow string) - semi-chords of the circle. Later, the concept was reduced to the word "jiva". Arab mathematicians used the term "jaib" (bulge).
What about cos? This relationship is much younger. The concept is an abbreviation for the Latin expression completely sinus, which in translation sounds like an additional sine (sine of an additional arc).
The modern short Latin designations sin and cos were introduced by William Oughtred in the 7th centuryand enshrined in the works of Euler.
What is a right triangle?
Since sin and cos are the ratios of the values of this figure, you need to know what it is. This is a type of triangle in which one of the angles is right, that is, it is 90 degrees. The legs are called the sides adjacent to the right angle (they lie opposite the sharp ones), and the hypotenuse is the opposite side.
They are connected by the Pythagorean theorem.
Definitions of sine and cosine
sin is the ratio of the opposite leg to the hypotenuse.
cos is the ratio of the adjacent leg to the hypotenuse.
Knowing the numerical values of the sides of the triangle, you can determine both of these values.
If we consider a unit circle centered at the point (0, 0) of the Cartesian coordinate system, then, taking a point on the abscissa axis and turning it by an acute angle alpha, we lower the perpendicular to the abscissa axis. The length of the leg adjacent to the hypotenuse in the resulting right triangle will be equal to the abscissa of the point.
Consequently, determining the acute angle in this figure in terms of the ratio of the sides cos(sin) is equivalent to finding the cosine (sine) of the angle of rotation with alpha ranging from 0 to 90 degrees.
What are these trigonometric functions for?
It is known that the sum of the angles in a right triangle is 180 degrees. So, knowing two angles, you can find the third one. ViaPythagorean theorems find the value of either side from the other two. And their relationship through sin and cos will help if one angle and one any side are known.
The question of solving such a problem arose when compiling maps of the starry sky, when it was impossible to accurately measure all quantities.
On the other hand, sin and cos ratios are trigonometric functions of angle. If its value is known, then with the help of special tables it will be possible to find all the necessary indicators.
