Trigonometry is the mathematical science of the trigonometric functions sin and cos. These relations are basic concepts; without understanding them, it will not be possible to learn something new in this area. This is 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 relations of segments of triangles. In ancient Rome, Menelaus explored them. The mathematician Ariabhata from India also defined these concepts. He connected the calculations of the sine with the "archajives" (literal translation - half a bowstring) - hemichords of a circle. Later, the concept was reduced to the word "jiva". Arab mathematicians used the term "jaib" (bulge).
What about cos? This attitude is much younger. The concept is an abbreviation of 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 Otred in the 7th century and are fixed in the writings of Euler.
What is a right triangle?
Since sin and cos are the ratios of the values of this figure, it is necessary to know what it is. This is a view of a triangle in which one of the corners of the line is 90 degrees. The legs adjacent to the right corner (lying opposite the sharp) are called the legs, and the opposite side is called the hypotenuse.
They are interconnected by the Pythagorean theorem.
Sine and Cosine Definitions
sin is the ratio of the opposite side to hypotenuse.
cos is the ratio of the adjacent leg to hypotenuse.
Knowing the numerical values of the sides of the triangle, both of these quantities can be determined.
If we consider a unit circle centered at a point (0,0) of the Cartesian coordinate system, then, taking a point on the abscissa axis and turning it by an acute angle alpha, lower the perpendicular to the abscissa axis. The length of the leg adjacent to the hypotenuse in the resulting right-angled triangle will be the abscissa of the point.
Therefore, the definition through the aspect ratio cos (sin) of the acute angle in this figure is equivalent to finding the cosine (sine) of the rotation angle with alpha lying in the range from 0 to 90 degrees.
What are these trigonometric functions for?
It is known that the sum of the angles in a right-angled triangle is 180 degrees. So, knowing two angles, you can find a third. Using the Pythagorean theorem, they find the value of either side in two other ways. And their relationship through sin and cos will help if one corner and one any side are known.
The question of solving this problem arose in compiling maps of the starry sky, when it was definitely impossible to measure all the quantities.
On the other hand, the ratios of sin and cos are trigonometric functions of the angle. If its value is known, then using special tables it will turn out to find all the necessary indicators.