Square relation: sin 2 (α)+cos 2 (α) =1tan 2 (α)+1= sec2 (α) cot2 (α)+1= CSC 2 (α) quotient. Sinα reciprocity relation: tan α cotα =1sin α CSC α =1cos α secα =1universal formula: sin α = 2tan (α/2)/[1+tan2 (α/2)]. [1+tan 2 (α/2)] tan α = 2 tan (α/2)/[1-tan 2 (α/2)] There are several commonly used inductive formulas: Formula1:Let α be an arbitrary angle, The values of the same trigonometric function with the angles of the same terminal side are equal: sin (2kπ+α) = sinα cos (2kπ+α) = cos α tan (2kπ+α) = tan α cot (2kπ+α) = tan α π+α The relationship between the trigonometric function values and α trigonometric function values: sin (π+α) =-sin α cos. = tanαcot(π+α)= cotα Formula 3: Relationship between trigonometric function value of arbitrary angle α and-α: sin (-α) = -tan α cot (-α) =-cot α Formula 4: The relationship between π-α and α trigonometric function value can be obtained by using Formula 2 and Formula 3: sin (π-α) = sin α cos (π (. =-sin α cos (2π-α) = cos α tan (2π-α) =-tan α cot (2π-α) =-cot α Formula 6: Relationship between π/2α and 3 π/2 α and α trigonometric function value: sin (π 2+α) =-sin α tan (π/2+α). The most commonly used formulas are: sin (a+b) = Sina * Cosb+Sinb * Cosasin (a-b) = Sina * Cosb-Sinb * Cosacos (a+b) = Cosa * Cosb-Sina * Sinbcos (a-b) = Cosa * Cosb+Sina *. = (tana+tanb)/(1-tana * tanb) tan (a-b) = (tana-tanb)/(1+tana * tanb) square relation: sin 2 (α)+cos 2 (α) = 6544. +1 = CSC 2 (α) product relation: sin α = tan α * cos α cos α = cot α * sin α tan α = sin α * sec α cot α = cos α * CSC α sec α = tan α * sec α * cot α reciprocal relation: tan α cot α =/kloc-0. Sinα CSC α =1cos α secα = 65438 In the right triangle ABC, the sine value of angle A is equal to the diagonal of the opposite side of angle A, the cosine is equal to the tangent of the diagonal of the adjacent side of angle A, and the trigonometric function is the trigonometric function of the sum and difference of two angles: cos (α+β) = cos α, cos β-sin α, sin β cos (α-β) = cos α，cos β+sin α，sin β sin (α β) = sin α，cos β，cos α， Sinβ Tan (α+β) = (1-tan α tan β) Tan (α-β) = (tan α-tan β)/(kloc-0/+tan α tan β) Auxiliary angle formula: asinα+bcosα = (A 2+B 2) (65438). Double angle formula: sin (2α) = 2sinα cosα = 2. -1=1-2sin (α/2 (α) tan (2α) = 2tanα/[1-tan2 (α)] Triple angle formula: sin (3α) = 3sinα-4sin3 (α) cos. =√(( 1-cosα)/2)cos(α/2)=√(( 1+cosα)/2)tan(α/2)=√(( 1-cosα)/( 1+cosα))= Sinα/( 1+cosα)=( 1-cosα)/ Sinα power-down formula Sin 2 (α) = (1-cos (2α)) Universal formula: Sinα = 2tan (α/2)/[1+tan2 (α/2)] cosα = [1-tan2 (α/2). Sum and difference formula of products: sin α cos β = (1/2) [sin (α+β)+sin (α-β)] cos α sin β = (1/2) [sin (α+β)-sin = 0, which is expressed by the exponent of trigonometric function in higher algebra. +z^3/3！ +z^4/4！ +…+z^n/n！ +… At this time, the domain of trigonometric function has been extended to the whole complex set. Trigonometric function as the solution of differential equation: for differential equation group y =-y ""; Y=y'''', there is a general solution q, which can prove that Q=Asinx+Bcosx, so we can also define trigonometric functions from this perspective. Supplement: Represented by the corresponding exponent, a similar function-hyperbolic function can be defined, which has many similar properties with trigonometric function, and both are very interesting. Special trigonometric function value A0 ` 30` 45` 60` 90` sina01/2 √ 2/2 √ 3/21√ 3/21/20 tana0 √ 3/365438. 30 trigonometric function calculation power series c0+c1x+c2x2+...+cnxn+... = ∑ cnxn (n = 0 ..∞) c0+c1(x-a)+c2 (x-a) 2+...+cn (x Taylor expansion (power series expansion method): f(x)=f(a)+f'(a)/ 1! *(x-a)+f''(a)/2！ *(x-a)2+...f(n)(a)/n！ *(x-a)n+ ... practical power series: ex= 1+x+x2/2! +x3/3！ +...+xn/n！ +...ln( 1+x)=x-x2/3+x3/3-...(- 1)k- 1*xk/k+...(| x | & lt 1) sinx=x-x3/3！ +x5/5！ -...(- 1)k- 1 * x2k- 1/(2k- 1)！ +...(-∞& lt； x & lt∞) cosx= 1-x2/2！ +x4/4！ -...(- 1)k*x2k/(2k)！ +...(-∞& lt； x & lt∞)arcsinx = x+ 1/2 * x3/3+ 1 * 3/(2 * 4)* X5/5+...(| x | & lt 1)arc cosx =π-(x+ 1/2 * x3/3+ 1 * 3/(2 * 4)* X5/5+...)(| x | & lt 1) arctanx=x-x^3/3+x^5/5-...(x≤ 1) sinhx=x+x3/3！ +x5/5！ +...(- 1)k- 1 * x2k- 1/(2k- 1)！ +...(-∞& lt； x & lt∞) coshx= 1+x2/2！ +x4/4！ +...(- 1)k*x2k/(2k)！ +...(-∞& lt； x & lt∞)arcsinhx = x- 1/2 * x3/3+ 1 * 3/(2 * 4)* X5/5-...(| x | & lt 1)arctanhx=x+x^3/3+x^5/5+...(| x | & lt 1) - .a0= / Kloc-0//π ∫ (π ..-π) (f (x)) dxan =1∫ (π ..-π) (f (x) cos NX) dxbn =1/π ∫. For example: tana = tgasin2a = 2sinacos2a = cosa2-sina2 =1-2sina2 = 2cosa2-1tan2a = 2tana/1-tana. I wish you progress!