Formula 1: Let α be an arbitrary angle and the values of the same trigonometric function with the same terminal edge are equal: sin (2kπ+α) = sinα k ∈ zcos (2kπ+α) = cosα k ∈ ztan (2kπ+α) = tanα k ∈ zcot (2k The relationship between the trigonometric function values of π+α and α: sin (π+α) =-sin α k ∈ z cos (π+α) =-cos α k ∈ z tan (π+α) = tan α k ∈ z cot (π+α) = cot α k ∈. =-cscα k∈z Formula 3: Relationship between any angle α and trigonometric function value of-α: sin (-α) =-sin α cos (-α) = cos α tan (-α) =-tan α cot (-α) =-cot α sec (-α) = secα CSC (-α) =-cscα 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-α) =-cos α tan (π-α) =-tan α cot (π-α) =-cot α sec (π-α) =-sec. =cscα Formula 5: Using Formula 1 and Formula 3, the relationship between trigonometric function values of 2π-α and α can be obtained: sin (2π-α) =-sin α cos (2π-α) = cos α tan (2π-α) =-tan α cot (2π-α) =-cot α sec (. = cosαcos(π/2+α)=-sinαtan(π2-α)= sinαtan(π/2-α)= cotαcot(π/2-α)= tanαsec(π/2-α)= CSCαCSC(π/2-α)= secαsin(3π/2+α)=-cosαcos(3π/2+α)= sinαtan(3π/2+α) =-COT α COT α (3 π/2+α) =-tan α sec (3 π/2+α) = CSC α CSC (3 "odd and even" refers to the parity of a multiple of π/2, and "variable and invariant" refers to the change of the name of a trigonometric function: "variable" refers to the change of sine into cosine, and "variable" refers to the change of sine into cosine. (and vice versa) The meaning of "symbol looking at quadrant" is: take angle α as an acute angle, regardless of the quadrant where angle α is located, look at what quadrant angle N (π/2) α is, and then get whether the right side of the equation is positive or negative. Symbolic judgment formula: "a full pair; Two sinusoids; Cut in twos and threes; Four cosines ". The meaning of this formula 12 is: the four trigonometric functions at any angle in the first quadrant are "+"; In the second quadrant, only the sine is "+",and the rest are "-"; In the third quadrant, only the tangent and cotangent are "+",and the rest are "-"; In the fourth quadrant, only cosine is "+",others are "-". "ASCT" is opposite to Z, which means that "all", "sin", "cos" and "tan" are trigonometric functions, corresponding to the quadrant occupied by the letter Z in reverse. Edit the knowledge of other trigonometric functions in this paragraph. The reciprocal relation of trigonometric function with the same angle is tan α cotα =1sin α CSC α =1cos α secα =1quotient sin α/cos α = tan α = secα/CSC α cosα = cotα/secα square relation sin 2 (α)+cos 2 (α) =/. +tan 2 (α) = sec 2 (α)1+cot 2 (α) =1The two functions on the diagonal of the reciprocal relation are reciprocal; The function value of any vertex of the quotient relation hexagon is equal to the product of the function values of two adjacent vertices. (Mainly the product of trigonometric function values at both ends of two dotted lines). From this, the quotient relation can be obtained. Square relation In a triangle with hatched lines, the sum of squares of trigonometric function values of the top two vertices is equal to the square of trigonometric function values of the bottom vertex. Sum and difference formula sin (α+β) = sin α cos β+cos α sin β sin (α-β) = sin α cos β-cos α sin β cos (α+β) = cos α cos β-sin α sin β cos (α-β) = cos α cos β+sin α sin β tan (α+β) = (tan α+) > tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)sin 2α= .- 1 = 1-2 SIN 2(α)tan 2α= 2 tanα/( 1-tan 2α))SIN 2(α/2)=( 1-cosα)。 = (1-cos α)/(1+cos α) tan (α/2) = (1-cos α)/sin α = sin α/1+cos α general formula sin α = 2 tan (α/2)/. )/(1-tan2 (α/2)) trigonometric function sinα+sinβ = 2sin ((α+β)/2) cos ((α-β)/2) sinα-sinβ. SIN((α-β)/2) trigonometric function sum difference formula sin α-cos β = 0.5 [sin (α+β)+sin (α-β)] cos α-sin β = 0.5 [sin (.