Triangle 1 + triangle 2 = 11 circle 1 + circle 2 = 22 positive 1 + positive 2 = 33 triangle 1 + circle 2 = 12 positive 1 + triangle 2 = 31 then positive 1 + three 2 =?

Triangle 1 + triangle 2 = 11 circle 1 + circle 2 = 22 positive 1 + positive 2 = 33 triangle 1 + circle 2 = 12 positive 1 + triangle 2 = 31 then positive 1 + three 2 =?

sin(A+B)=sinAcosB+cosAsinB
--->sin2A=2sinAcosA
cos(A+B)=cosAcosB-sinAsinB
--->cos2A=(cosA)^2-(sinA)^2=(1-(sinA)^2-(sinA)^2=1-2(sinA)^2=2(cosA)^2-1.
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
--->tan2A=2tanA/[1-(tanA)^2]
In the double angle formula of cosine, the half angle formula is obtained by solving the equation
cosx=1-2[sin(x/2)]^2
---≫ sin (x / 2) = + '- √ [(1-cosx) / 2] the sign is determined by the quadrant of (x / 2), the same below
cosx=2[cos(x/2)]^2
--->cos(x/2)=+'-√[1+cosx)/2]
The two sides of the two formulas are divided separately to get the result
tan(x/2)=+'-√[(1-cosx)/(1+cosx)].
And Tan (x / 2) = sin (x / 2) / cos (x / 2)
=2[sin(x/2)]^2/[2sin(x/2)cos(x/2)]
=(1-cosx)/sinx
=sinx/(1+cosx).
trigonometric function
Trigonometric function is a kind of transcendental function in elementary function in mathematics. Its essence is the mapping between the set of any angle and the variable of a ratio set. The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain. Another definition is in the right triangle, Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definition to complex number system
Because of the periodicity of trigonometric function, it does not have inverse function in the sense of single valued function
Trigonometric functions have important applications in complex numbers. In physics, trigonometric functions are also commonly used tools
It has six basic functions
Function name sine cosine tangent cosecant secant cosecant
Sign sin cos Tan cot sec CSC
Sine function sin (a) = A / h
Cosine function cos (a) = B / h
Tangent function Tan (a) = A / b
Cotangent function cot (a) = B / A
Secant function sec (a) = H / b
Cosecant function CSC (a) = H / A
The basic relations between trigonometric functions of the same angle are as follows
·Square relation:
sin^2(α)+cos^2(α)=1
tan^2(α)+1=sec^2(α)
cot^2(α)+1=csc^2(α)
·Business relationship:
tanα=sinα/cosα cotα=cosα/sinα
·Reciprocal relationship:
tanα·cotα=1
sinα·cscα=1
cosα·secα=1
The formula of trigonometric function identity deformation is as follows
·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)
·Double angle formula:
sin(2α)=2sinα·cosα
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
·Universal 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)]
·The formula of product sum difference is as follows
sinα·cosβ=(1/2)[sin(α+β)+sin(α-β)]
cosα·sinβ=(1/2)[sin(α+β)-sin(α-β)]
cosα·cosβ=(1/2)[cos(α+β)+cos(α-β)]
sinα·sinβ=-(1/2)[cos(α+β)-cos(α-β)]
·Sum difference product formula:
sinα+sinβ=2sin[(α+β)/2]cos[(α-β)/2]
sinα-sinβ=2cos[(α+β)/2]sin[(α-β)/2]
cosα+cosβ=2cos[(α+β)/2]cos[(α-β)/2]
cosα-cosβ=-2sin[(α+β)/2]sin[(α-β)/2]
Angular function
Teaching objectives of this chapter
1. (1) the concept of any angle and the radian system. Correctly represent the quadrant angle, interval angle and the angle with the same end edge, and skillfully convert the angle system and radian system
(2) The definition of trigonometric function of any angle, the sign change law of trigonometric function, and the meaning of trigonometric function line
2. (1) the basic relation and induced formula of trigonometric function of the same angle
(2) Given trigonometric function value angle
3. Image of functions y = SiNx, y = cosx, y = TaNx and y = asin (ω x + φ) and "five point method" drawing, image method transformation, understand the physical meaning of a, ω and φ
4. Domain of definition, range of value, parity, monotonicity and periodicity of trigonometric function
5. Trigonometric function and double angle formula of sum and difference of two angles, can correctly use trigonometric formula to simplify, evaluate and prove identity of simple trigonometric function formula
This chapter includes three parts: trigonometric function of arbitrary angle, trigonometric function of sum and difference of two angles, image and property of trigonometric function
Trigonometric function is an important part of middle school mathematics. It is not only a tool to solve practical problems in production and scientific research, but also a basis for further learning other related knowledge and higher mathematics. It has a wide range of applications in physics, astronomy, surveying and other applied technology disciplines
Reference: Sina
Respondent: hzglsd - Assistant Level 2 10-17 22:10