According to the ancients, sine is
thigh
and
bowstring
The proportion of.
As the old saying goes.
delete
The "string" in "three strands, four strings and five" is
right triangle
The hypotenuse is at.
The thigh is a human thigh, which is very long. The ancients called the long right side of a right triangle "thigh". Right triangle, thighs should stand straight.
Sine is the ratio of chord to strand,
cosine
Is the ratio of the remaining right angle edge to the chord.
Sine = unit head/chord length
Put Pythagoras' string in it
circle
The inch string is
circumference
What is the biggest chord in the connection between two points?
diameter
Put the chord of a right triangle on the diameter, the chord is long, that is, sine, and the hook is short, that is, cosine-cosine.
According to modern theory, sine is the ratio of the opposite side to the hypotenuse of a right triangle.
The modern sine formula is
commit a crime
=
The opposite side of a right triangle is longer than the hypotenuse.
As shown in the figure, the hypotenuse is r, the opposite side is y, and the adjacent side is X.
The angle α between the hypotenuse and the adjacent edge.
sin=y/r
Whether y>x or y≤x
No matter how big or small A is, it can be any size.
The maximum sine value is 1.
The minimum value is-1
trigonometric function
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, which is called the angle A..
Tangent, written as tanA.
That is tanA= angle a.
The opposite/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 α, 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 α, and is recorded as cosA.
That is, cosA= the adjacent side of angle A/the hypotenuse of angle A..
Correlation formula
Sum of squares relation
sin^2α+cos^2α= 1
Product relationship
sinα=tanα×cosα
cosα=cotα×sinα
tanα=sinα×secα
Relationship of quotient
sinα/cosα=tanα=secα/cscα
Sum angle formula
sin(α β)=sinα cosβ cosα sinβ
sin(α+β+γ)= sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ-sinαsinβsinγ
half-angle formula
sin(2α)=2sinα cosα=2/(tanα+cotα)
sin(3α)=3sinα-4sin？ (α)=4sinα sin(60+α)sin(60-α)
sin(α/2)= √(( 1-cosα)/2)
other
sinx=[e^(ix)-e^(-ix)]/(2i)
(from Taylor series)
commit a crime
x
=
x-x3/3！ +x5/5！ -...(- 1)k- 1 * x2k- 1/(2k- 1)！ + ...
(-∞& lt； x & lt∞)
(series expansion)
(sinx)'=cosx
(derivative)
Simply put, sine is odd function and cosine is even function. You can directly change the x of F[X] into -X to see if the other end of the equation is the same as the original or its inverse. It doesn't matter.