Question 1: What does trigonometric function mean? ! To tell you the truth, I have been studying trigonometric functions for a long time. It is also known that sinA (the ratio of the opposite side of angle A to the hypotenuse of this triangle) cosA (the ratio of the adjacent side of angle A to the hypotenuse of this triangle) tanA (the ratio of the opposite side to the adjacent side of angle A) middle school usually appears in the form of a triangular solution. Give you a few conditions. Understand the relationship between other edges and corners. But the meaning of high school has been greatly expanded. Especially complicated. But as long as you lay a good foundation, study hard now. Anyway, it's not a big problem, we just need to do more and practice more. Maritime tactics.

Question 2: What does trigonometric function mean? Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between * * * of any angle and * * * of proportional 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.

basic content

It has six basic functions (elementary basic representation):

Function name sine cosine tangent cotangent secant cotangent

Sinθ=y/r

Cosine function cosθ=x/r

Tangent function tanθ=y/x

Cotangent function cotθ=x/y

Secθ secθ=r/x

Cotangent function csθ= r/y

And two functions that are not commonly used and easily eliminated:

Positive vector function version θ = 1-cosθ

Vector function vercosθ = 1-sinθ

The basic relationship between trigonometric functions with the same angle;

? Square relation:

sin^2(α)+cos^2(α)= 1

tan^2(α)+ 1=sec^2(α)

cot^2(α)+ 1=csc^2(α)

? Product relationship:

sinα=tanα*cosα cosα=cotα*sinα

tanα=sinα*secα cotα=cosα*cscα

secα= tanα* CSCαcsα= secα* cotα

? Reciprocal relationship:

tanα？ cotα= 1

sinα？ cscα= 1

cosα？ secα= 1

Constant deformation formula of trigonometric function;

? Trigonometric function of sum and difference of two angles;

cos(α+β)=cosα？ cosβ-sinα？ sinβ

cos(α-β)=cosα？ cosβ+sinα？ sinβ

sin(α β)=sinα？ cosβ cosα？ sinβ

tan(α+β)=(tanα+tanβ)/( 1-tanα？ tanβ)

tan(α-β)=(tanα-tanβ)/( 1+tanα？ tanβ)

? Auxiliary angle formula:

Asinα+bcosα = (A2+B2) (1/2) sin (α+t), where

sint=B/(A^2+B^2)^( 1/2)

cost=A/(A^2+B^2)^( 1/2)

? Double angle formula:

sin(2α)=2sinα？ Coase α

cos(2α)=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)

tan(2α)=2tanα/[ 1-tan^2(α)]

? Triple angle formula:

sin3α=3sinα-4sin^3(α)

cos3α=4cos^3(α)-3cosα

? Half-angle formula:

sin^2(α/2)=( 1-cosα)/2

cos^2(α/2)=( 1+cosα)/2

tan^2(α/2)=( 1-cosα)/( 1+cosα)

tan(α/2)= sinα/( 1+cosα)=( 1-cosα)/sinα

? General formula:

sinα=2tan(α/2)/[ 1+tan^2(α/2)]

cosα=[ 1-tan^2(α/2)]/[ 1+tan^2(α/2)]

tanα=2tan(α/2)/[ 1-tan^2(α/2)]

? Product sum and difference formula:

sinα？ cosβ=( 1/2)[sin(α+β)+sin......& gt& gt