What does sine mean and what is the definition of sine

1. In a right-angled triangle, the sine of a certain angle is the ratio of the opposite side of the angle to the hypotenuse.

2. Take a special case, the side corresponding to the right angle is the hypotenuse, so the ratio is 1, so the sine of 90° is 1

What is the definition of sine.

The ratio of the opposite side of angle a to the hypotenuse is called the sine of angle a and is denoted as sina, i.e. sina = the opposite side of angle a hypotenuse.

In ancient times, a sine was the ratio of strands to strings.

The "string" in the ancient saying of "hook three strands, four strings and five" is the hypotenuse in the right triangle.

The strand is the human thigh, long, and the ancients called the right-angled side of the right triangle "strand"; The right triangle should be placed upright, and the thighs should be standing straight.

The sine is the ratio of the strands to the chord, and the cosine is the ratio of the remaining right-angled side to the chord.

Sine = strand length Chord length.

The Pythagorean string is placed in a circle. A string is a line connecting two points around a circle. The largest chord is the diameter.

Put the right triangle string on the diameter, the strand is the long string, that is, the sine, and the hook is the short string, that is, the remaining string, the cosine.

In modern terms, a sine is the ratio of the opposite side of a right triangle to the hypotenuse.

The modern sine formula is.

The opposite side of a right-angled triangle is more hypotenuse than the hypotenuse.

The angle between the hypotenuse and the adjacent edge a

sin=y/r

Regardless of y>x or yx

No matter how big or small the A is, it can be any size.

The maximum value of the sine is 1

The minimum value is -1

Trigonometric function. Trigonometric functions are a class of functions in mathematics that belong to the transcendental functions of elementary functions. Their essence is a mapping between a set of arbitrary angles and a set of variables with a ratio.

The usual trigonometric function is defined in a planar Cartesian coordinate system, which defines the entire field of real numbers. Another definition is in a right triangle, but not completely. Modern mathematics describes them as the limits of an infinite series of numbers and the solution of differential equations, extending their definition to complex systems.

Due to the periodic nature of trigonometric functions, it does not have an inverse function in the sense of a single-valued function.

Trigonometric functions have important applications in complex numbers. In physics, trigonometric functions are also commonly used tools.

In RT ABC, if the acute angle A is determined, then the ratio of the opposite side of the angle A to the adjacent side is determined at will, and this ratio is called the angle A

tangent, denoted as tana

i.e. tana = angle a

The adjacent edge of the opposite corner a.

The sine is inRight triangle, the length of the opposite edge is greater than the length of the upper hypotenuse.

The sine of any acute angle is equal to its coangle.

, the cosine of any acute angle is equal to the sine of its cosine.

Sinusoidal sin can also be understood as an isosceles triangle with a top angle number of .

The ratio to the area of the unit isosceles right triangle.

sin30°=1╱2

sin45°=√2╱2

sin60°=√3╱2

sin90°=1

sin180°=0

sin0°=0

sin270°=-1

Meaning:

Generally, in Cartesian coordinate systems.

, given a unit circle, for any angle , so that the vertex of the angle coincides with the origin, the beginning edge coincides with the non-negative semi-axis of the x-axis, and the terminal edge intersects the unit circle at the point p(u,v), then the ordinate v of the point p is called the sinusoidal function of the angle.

Denote as v=sin.

Typically, we use x to represent the argument.

That is, x denotes the size of the angle, and y denotes the value of the function, so that we define the trigonometric function y=sinx for any angle, which defines the domain.

is the whole real number, the value range.

for [-1,1].

<> sine is the value of the opposite side in a right triangle that is longer than the upper hypotenuse. The sine of any acute angle is equal to the cosine of its coangle, and the cosine of any acute angle is equal to the sine of its coangle.

Sine: In RT ABC, C=90°, we call the ratio of the opposite side of the acute angle A to the hypotenuse as the sine of A, which is denoted as sina, i.e.

sina = the opposite side of a hypotenuse = a c

Cosine: We call the ratio of the adjacent edge of a to the hypotenuse of a cosine, which is denoted as cosa, i.e.

cosa= adjacent edge of a hypotenuse = b c

Tangent: The ratio of the opposite side of a to the adjacent side is called tangent of a, which is denoted as tana, i.e.

tana= the opposite side of a and the adjacent edge of a = a b

There is also a formula for tana.

tana=sina/cosa

Sine function. The most basic case is that sina represents the opposite and hypotenuse of the acute angle A in the right angle of ABC.

The ratio of sina=bc ab is different, because the ratio is different at different acute angles, so it constitutes a functional relationship. For example, sin30 degrees = 1 2.

sin 360 encyclopedia.

in a right triangle.

, The ratio of the opposite side of a (non-right angle) to the hypotenuse is called the sine of a, so it is recorded as sina, that is, sina = the opposite side of a The hypotenuse of a In ancient times, the sine is the ratio of strands to strings. The "string" in the ancient saying of "hook three strands, four strings and five" is the hypotenuse in the right triangle. The strand is the human thigh, long, and the ancients called the right-angled side of the right triangle "strand"; A square right-angled triangle with the thighs standing straight.

A sine is the ratio of the opposite side (not at right angles) to the hypotenuse, the cosine.

is the ratio of the adjacent edge of a (non-right angle) to the hypotenuse. The Pythagorean string is placed in a circle. A string is a line connecting two points around a circle. The largest chord is the diameter. Put the right triangle string on the diameter, the strand is the long string, i.e., the sine, and the hook is the short string, i.e., the cosine.

According to modern terms, a sine is the ratio of the opposite side of a right triangle (not a right angle) to the hypotenuse, that is, the opposite side of the hypotenuse.

y=asin(x+) is called the sinusoidal function.

Sinusoidal function analytical: y=asin( x+ )h The influence of each constant value on the function image:

Initial phase spike manuscript position): determine the waveform and x-axis position or the lateral movement distance (left plus right minus).

Determine the period Sakura (minimum positive period t=2 |.)

a: Determines the peak value (i.e., the multiple of longitudinal stretch compression).

h: Represents the position relationship of the waveform on the y-axis or the longitudinal movement distance (plus up and down minus), and the drawing method uses the "five-point method" to plot.

Five-point plotting, i.e., when x+ takes 0, 2, ,3 2,2 respectively, the value of y.

1. Sinusoidal sin, is the abbreviation of sine, pronunciation: English [sa n], American [sa n].

2. Cosine cos, is the abbreviation of cosine, pronunciation: English [ k sa n], Mei [ ko sa n].

3. Tangent tan, is the abbreviation of tangent, pronunciation: Yingxiangdong [ t nd nt], Mei [ t nd nt].

In a right-angled triangle, the sine is the ratio of the opposite side of a certain angle (non-right angle) of the right-angled triangle to the hypotenuse, that is: the hypotenuse of the edge of the banquet bush; The cosine is the ratio of the adjacent edge to the hypotenuse of a non-right angle; Tangent is the ratio of an edge to an adjacent edge.

In any right triangle, the ratio of the opposite side to the adjacent edge corresponding to is called the tangent of the angle tan. If you put in a Cartesian coordinate system, you will have tan = y on the opposite edge of the adjacent edge. In Cartesian coordinate systems, it corresponds to the slope k of a straight line.

Sine sina = the opposite side of a hypotenuse, which can be simply written as sin=opposite side than hypotenuse.

Application: In a right-angled triangle, non-right-angled), sin = the hypotenuse of the opposite side.

sin(α+sinα·cosβ+cosα·sinβsin(α-sinα·cosβ-cosα·sinβsin(2a)=2sina*cosa

Sine sina = the opposite side of a hypotenuse, which can be simply written as sin=opposite side than hypotenuse.

Application: In a right-angled triangle, non-right-angled), sin = the hypotenuse of the opposite side.

sin(α+sinα·cosβ+cosα·sinβsin(α-sinα·cosβ-cosα·sinβsin(2a)=2sina*cosa

sin: refers to the ratio of the opposite side to the hypotenuse of non-right angles in a right triangle called the sine of , denoted as sin, and the sine is the ratio of the hook to the chord. The "string" in the ancient saying of "hook three strands, four strings and five" is the hypotenuse in the right triangle.

The strand is the human thigh, and the ancients called the right-angled side of the right triangle "strand".

Application: In a right-angled triangle, non-right-angled), sin = the hypotenuse of the opposite side.

sin(α+sinα·cosβ+cosα·sinβsin(α-sinα·cosβ-cosα·sinβsin(2a)=2sina*cosa