Y=sinx is the increasing function on [2kπ-π/2, 2kπ+π/2], k ∈ z.
It is a decreasing function on [2kπ+π/2, 2kπ+3π/2], k ∈ z.
Trigonometric function y=sin x, its domain is all real numbers, and its value range is [- 1, 1].
2. Cosine function
Y=cosx is a decreasing function on [2kπ, 2kπ+π], k ∈ z.
On [2kπ+π, 2kπ+2π], k∈Z is increasing function.
The domain of cosine function is a whole set of real numbers, and the range of values is [- 1, 1]. It is a periodic function with a minimum positive period of 2π.
Extended data
Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables.
The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.
Because of the periodicity of trigonometric function, it does not have the inverse function in the sense of single-valued function. Trigonometric functions have important applications in complex numbers. Trigonometric function is also a common tool in physics.
In RT△ABC, if the acute angle A is determined, then the ratio of the opposite side to the adjacent side of the angle A is determined accordingly. This ratio is called the tangent of angle A, and is written as tanA, that is, tanA= the opposite side of angle A/the adjacent side of angle A. ..
Similarly, in RT△ABC, if the acute angle A is determined, the ratio of the opposite side to the hypotenuse of the angle A is determined accordingly. This ratio is called sine of angle A, and is recorded as sinA, that is, sinA= the opposite side of angle A/the hypotenuse of angle A. ..
Similarly, in RT△ABC, if the acute angle A is determined, the ratio of the adjacent side to the hypotenuse of the angle A is determined accordingly. This ratio is called cosine of angle A, and it is recorded as cosA, that is, cosA= adjacent side of angle A/hypotenuse of angle A. ..
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