What is a sine

What is a sine

On a rectangular triangle as the simplest of polygons, different men of science perfected the knowledge in the field of trigonometry still in those days when nobody even called this field of mathematics such word. Therefore to specify the author who revealed regularities in ratios of lengths of the parties and sizes of corners in this flat geometrical figure today it is not possible. Such ratios are called trigonometrical functions and divided into several groups, "direct" functions conditionally are considered as basic of which. Only two functions and one of them - a sine are referred to this group.

Instruction

1. By definition one of corners is equal in a rectangular triangle 90 °, and owing to the fact that the sum of its corners in Euclidean geometry is obliged to be equal 180 °, two other corners are sharp (i.e. less than 90 °). Regularities of ratios of these corners and lengths of the parties also describe trigonometrical functions.

2. The function called a sine of an acute angle defines a ratio between length of two parties of a rectangular triangle, one of which lies opposite to this acute angle, and another adjoins it and lies opposite to a right angle. As the party lying opposite to a right angle in such triangle is called a hypotenuse, and two others - legs, function definition a sine can be formulated as a ratio between lengths of an opposite leg and hypotenuse.

3. Except such simplest definition of this trigonometrical function exist also more difficult today: through a circle in the Cartesian coordinates, through ranks, through solutions of the differential and functional equations. This function is continuous, that is any number - from infinitely negative to infinitely positive can be her arguments ("the field of definitions"). And the maximum and a minimum of values of this function are limited with a range from-1 to +1 are "area of its values". The minimum value accepts a sine at coal in 270 ° that there correspond 3/2 numbers of Pi, and maximum it turns out at 90 ° (½ from Pi). Zero values of function become at 0 °, 180 °, 360 °, etc. From all this follows that the sine is function periodic and its period is equal 360 ° or to the doubled Pi's number.

4. For practical calculations of values of this function from the set argument it is possible to use the calculator - the absolute majority of them (including the program calculator which is built in the operating system of your computer) has the corresponding option.

Author: «MirrorInfo» Dream Team


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