What are the concepts of trigonometric functions? What are trigonometric functions?

Next to the trigonometric function sail are: sine function, cosine function, tangent function, cotangent function, secant function, cosecant function rollover, and the positive and negative cases of each quadrant are as follows: (the format is "quadrant" or -").

Sinusoidal function: y=sinx, one +, two +, three -, four -;

Cosine function: y=cosx, one +, two -, three -, four +;

Tangent function: y=tanx, one +, two -, three +, four -;

Cotangent function: y=cotx, one +, two -, three +, four -;

Chia sedan cut function: y=secx, one +, two -, three -, four +;

Cosecant function: y=cscx, one +, two +, three -, four -.

Trigonometric functionsIt is defined as one of the basic elementary functions, which is a function with the angle as the independent variable, and the angle corresponds to the coordinates of the intersection point of the terminal edge of any angle with the unit circle or its ratio as the dependent variable.

Trigonometric functions are used in the study of triangles.

and the properties of geometric shapes, such as circles, play an important role and are also fundamental mathematical tools for the study of periodic phenomena.

in mathematical analysis.

trigonometric functions are also defined as infinite series or solutions to specific differential equations, allowing their value to be extended to arbitrary real values, even complex values.

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.

Basic elementary content.

It has six basic functions (elementary basic representations):

The name of the function. Sine.

Cosine. Tangent.

Cotangent. Secant.

Cosecant. Sine function.

sinθ=y/r

Cosine function. cosθ=x/r

Tangent function. tanθ=y/x

Cotangent function. cotθ=x/y

Secant function. secθ=r/x

Cosecant function. cscθ=r/y

and two functions that are not commonly used and tend to be obsolete:

Positive vector function. versinθ

1-cosθ

Covector function. vercosθ

1-sinθ

The basic relationship between the same angle trigonometric functions:

Sin 2 ( ) Cos 2 ( ) = 1tan 2 ( ) 1 = sec 2 ( ).

cot^2(α)1=csc^2(α)

product relation: sin = tan *cos

cosα=cotα*sinα

tanα=sinα*secα

cotα=cosα*cscα

secα=tanα*cscα

cscα=secα*cotα

Reciprocal relation: tan ·cot = 1

sinα·cscα=1

cosα·secα=1

In the right triangle ABC, the sine of angle A is equal to the opposite side of angle A, and the cosine is equal to the adjacent side of angle A.

The tangent is equal to the opposite side of the adjacent edge

In mathematics, trigonometry.

Also called a circular function) is a function of angles; They are important in studying triangles and modeling periodic phenomena and many other applications. Trigonometric function is usually defined as the ratio of the two sides of a right triangle containing this angle, and can also be defined equivalently as the length of various line segments on a unit circle. More modern definitions express them as infinite series or solutions to specific differential equations, allowing them to extend to arbitrary positive and negative values, even complex values.

Trigonometric functions belong to a class of functions in mathematics that are transcendental functions in elementary functions. They are essentially a mapping between a set of arbitrary angles and a set of variables with a ratio. Since trigonometric functions are periodic, they do not have an inverse function in the sense of a monographed function.

Trigonometric functions have important applications in complex numbers and are commonly used tools in physics.

Defining sin as y:1 or y:r is essentially the same and reasonable.

Define sin as y, which is more concise in form. Define the domain: sine function y=sinxx r cosine function y=cosx

x r tangent function y=tanx

x≠kπ+π/2，k∈z

The cotangent function y=cotx

x≠kπ，k∈z

The secant function y=secx

x≠kπ+π/2，k∈z

Cosecant function y=cscx

x≠kπ，k∈z

Trigonometric function is one of the basic elementary functions, which is a function in which the angle (the most commonly used radian system in mathematics, the same below) is the independent variable, and the angle corresponds to the coordinate of the final edge of any angle and the intersection point of the unit circle or its ratio as the dependent variable. It can also be defined equivalently in terms of the length of the various line segments related to the unit circle.

Trigonometric functions are used in the study of triangles.

and the properties of geometric shapes, such as circles, play an important role and are fundamental mathematical tools for the study of periodic phenomena. In mathematical analysis, trigonometric functions are also defined as infinite series or solutions to specific differential equations, allowing their values to be extended to arbitrary real values, even complex values.

Common trigonometric functions include sinusoidal functions.

Cosine function and hungry cherry tangent function.

In other disciplines such as navigation, surveying and mapping, engineering, etc., cotangent functions are also used.

secant function, cosecant function, positive judgment vector function, cosagittal function, semi-regular vector function, semi-cosagittal function, and other trigonometric functions. The relationship between different trigonometric functions can be determined by geometrical intuition, or by calculation, and is called trigonometric identities.

Trigonometric functions are: sine function, cosine function, tangent function, cotangent function, secant function, cosecant function, and cosecant function in each quadrant as follows: (expressed in the format "quadrant" or -").

Sinusoidal function: y=sinx, one +, two +, three -, four -;

Cosine function: y=cosx, one +, two -, three -, four +;

Tangent function: y=tanx, one +, two -, three diggings +, four -;

Cotangent function: y=cotx, one +, two -, three +, four -;

secant function: y=secx, one +, two -, three -, four +;

Cosecant function: y=cscx, one +, two +, three -, four -.

Common trigonometric functions include sine, cosine, and tangent. In other disciplines such as navigation, surveying and mapping, and engineering, other scattered trigonometric functions such as cotangent function, secant function, cosecant function, sagittal function, cosagittal function, semi-sagittal function, semi-cosagittal function, and other scattered trigonometric functions are also used.

Concept

Trigonometric function is one of the basic elementary functions, which is a function in which the angle (the most commonly used radian system in mathematics) is the independent variable, and the angle corresponds to the coordinates of the intersection point of the terminal edge of any angle with the unit circle or its ratio as the dependent variable. Common trigonometric functions include sine, cosine, and tangent.

Formula

Basic nature. In the Cartesian coordinate system, the radius of is 1, and the trigonometric function of any angle is defined as follows:

Sine: The ratio of the ordinate of the intersection of the angle and the unit circle a to the radius of the circle is called the sinusoid.

Cosine: The ratio of the coarse abscissa of the angle to the radius of the circle at the intersection point a of the unit circle is called the cosine.

Tangent: The ratio of the ordinate to the abscissa of the intersection point a of the angle and the unit circle is called the tangent. Knowledge development.

Define the trigonometric function of an arbitrary angle with the coordinates of a point on the final edge of the angle.

Explanation of trigonometric functions.

Let the three sides of a right triangle with an acute angle be a, b, and c (as shown in the figure), and the ratio between the lengths of each side, such as a c, b c, a b, b a, and a b, c a, are respectively called the sine, cosine, tangent, cotangent, secant, and cosecant of the angle, and are denoted as sin, cos, tg (or tan), ctg (or cot), sec, csc (or cosec). When they change, they all change with them, so that each of them is a function of , called a "trigonometric function". The coordinate method can also be used to extend the concept of trigonometric functions to exponents to arbitrary angles.

Word decomposition Explanation of triangle refers to an object that looks like a triangle, a triangle, a face, a triangle, a pillow triangle, a nickel-chromium triangle, a detailed explanation of the abbreviation of trigonometry. Three horns. "The Classic of Mountains and Seas, The Classic of the South Mountains" "Five hundred miles to the east, the mountain that has been prayed for, there are many gold and jade on it, and there are many rhinos and rhinos under it" Jin Guo Pu Note:

The rhinoceros resembles a buffalo ......Trigonometry: One at the top, one Explanation of a function One of the two quantities related to each other, their relation to the values of one quantity corresponds to the values of another quantity Explained in detail is called a causal variable. Mathematical noun .

In two numbers that are related to each other, if the number A changes, and the number B also changes with the change of the number A, then the number B is called a function of the number A. Such as a certain cloth per foot **one.