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) = sin α cos (2kπ+α) = cos α tan (2kπ+α) = tan α cot (2kπ+α) = cot α Formula 2: Let α be an arbitrary angle. Relationship between trigonometric function value of π+α and trigonometric function value of α: sin (π+α) =-sin α cos (π+α) =-cos α tan (π+α) = tan α cot (π+α) = cot α Formula 3: Relationship between trigonometric function value of arbitrary angle α and-α: sin (-α) = = The relationship between π-α and α trigonometric function value can be obtained: the relationship between sin (π-α) = sin α angular function value: sin (2π-α) =-sinα cos (2π-α) = cos α tan (2π-α) =-tan α cot (2π-α) =-cot α formula 6: π/. =-sin α tan (π/2+α) =-cot α cot (π/2+α) =-tan α sin (π/2-α) = cos α cos (π/α) The inductive formula can be summarized as follows: for the trigonometric function value of k π/2 α (k ∈ z), ① when k is even, ② When k is an odd number, the cofunction value corresponding to α is obtained, that is, sin→cos；; cos→sin； Tan → Kurt, Kurt → Tan. (even if it is odd, even if it is constant) and then consider α as an acute angle, add the sign of the original function value. For example: sin (2 π-α) = sin (4 π/2-α), and k = 4 is an even number, so we take sinα. When α is an acute angle, 2π-α ∈ (270,360), sin (2π-α) < 0, and the symbol is "-". So sin (2π-α) =-sin α The above memory formula is: odd even, and the sign depends on the quadrant. The symbol on the right side of the formula is that when α is regarded as an acute angle, the symbolic memory level of the original trigonometric function values in the quadrants of angles k 360+α (k ∈ z),-α, 180 α and 360-α remains unchanged; Symbols look at quadrants. How to judge the symbols of various trigonometric functions in four quadrants, you can also remember the formula "a full pair; Two sinusoids; The third is cutting; 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 "-"; The tangent function of the third quadrant is+and the chord function is-. In the fourth quadrant, only the cosine is "+",and the rest are "-". Other trigonometric functions: the basic relationship of trigonometric functions with the same angle 1. The reciprocal relation of the basic relation of trigonometric functions with the same angle: tan α cotα =1sin α CSC α =1cos α secα =1quotient relation: sin α/cos α = tan α = sec α. CSC α COS α/SIN α = COT α = CSC α/SEC α square relation: SIN 2 (α)+COS 2 (α) =11+Tan 2 (α) = Sec 2 (α)1+COT 2. Zuo Zheng, the right remainder and the regular hexagon of the middle 1 "are models. (1) Reciprocal relation: The two functions on the diagonal are reciprocal; (2) Quotient relation: the function value at any vertex of a hexagon is equal to the product of the function values at 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. (3) Square relation: In a triangle with hatched lines, the sum of squares of trigonometric function values on the top two vertices is equal to the square of trigonometric function values on the bottom vertex. The sum and difference formula of two angles 1. The formula of trigonometric function 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+tan β tan. (α+β) =—————1-tan α, tanβ, tan α-tan β (α-β) =—————1+tan α, tan β double angle formula; 3. Sine, Cosine and Tangent Formulas of Double Angles (formula for raising power and shrinking angle). -sin2 (α) = 2cos2 (α)-1=1-2sin2 (α) 2tan α tan2alpha = —————1-tan2 (α) sine of half angle formula, sine of half angle. =——— 21+cosα cos2 (α/2) =———— 21-cosα tan2 (α/2) =——1+cosα general formula χ general formula 2tan (χ)/kloc-. 2 tan α = —————— *, (because cos 2 (α)+sin 2 (α) = 1) and then divide the * fraction by cos 2 (α), you can get sin 2 α = tan2 α/( 1+tan. Similarly, the universal formula of cosine can be derived. By comparing sine and cosine, a general formula of tangent can be obtained. Triangle formula [6] sin3alpha = 3sinα-4sin3 (α) cos3alpha = 4cos3 (α)-3cosα-tan3 (α) tan3alpha =-1-3tan2. cos^3(α=(sin 2αcosα+cos 2αsinα)/(cos 2αcosα-sin 2αsinα)=(2 sinαcos 2(α)+cos 2(α)sinα-sin 3(α))/(cos 3(α)-cosαsin 2(α)get:tan 3α=(3 tanα-tan 3(α))/( / Kloc-0/-3tan2 (α)) sin3alpha = sin (2α+α) = sin2alpha cos+cos2alpha sin = 2sin trigonometric function; ⒎ and the differential product formula α+β α-β sinα+sinβ = 2sin-cos-22alpha+β-β sinα-sinβ. 2 α+β α-β cos α-cos β =-2 sin-2 2 product sum difference formula Χ product sum difference formula of trigonometric function sin α-cos β = 0.5 [sin (α+β)+sin (α-β)] cos α-sin β. Cos α cos β = 0.5 [cos (α+β)+cos (α-β)] sin α sin β =-0.5 [cos (α+β)-cos (α-β)] and derivation of differential product formula: First, we know that sin (a+b) = sin a * cos. Sin(a-b)=sina*cosb-cosa*sinb We add the two formulas to get sin(a+b)+sin(a-b)=2sina*cosb. So, SINA * COSB = (SIN (A+B)+SIN (A-B))/2 Similarly, if you subtract the two formulas, you get COSA * SINB = (SIN (A+B)-SIN (A-B))/2. Similarly, we also know that COSA (A+B) = COSA * COSB-SINA * SINB, COSA (A-B) = COSA * COSB+SINA * SINB. So, add the two formulas. We can get cos(a+b)+cos(a-b)=2cosa*cosb, so we can get cos * cosb = (cos (a+b)+cos (a-b))/2. Similarly, the subtraction of two expressions can get SINA * SINB =-(COS (A+B)-COS. We get four formulas of product and difference: Sina * cosb = (sin (a+b)+sin (a-b))/2cosa * sinb = (sin (a+b)-sin (a-b))/2cosa * cosb = (cos (a+b)+cos. Well, with the four formulas of product and difference, you only need one deformation to get the four formulas of product and difference. Let a+b be X and A-B be Y in the above four formulas, then a=(x+y)/2 and b=(x-y)/2 and express A and B with X respectively. Y, we can get four formulas of sum-difference product: sinx+siny = 2sin ((x+y)/2) * cos ((x-y)/2) sinx-siny = 2cos ((x+y)/2) * sin ((x-y)/2) cosx. Cosx-Cosy =-2 sin ((x+y)/2) * sin ((x-y)/2) Vector operation and addition AB+BC = AC, which is called triangle rule of vector addition. It is known that the two vectors OA and OB starting from the same point O are parallelogram OACB, and the diagonal OC starting from O is the sum of the vectors OA and OB. This calculation method is called parallelogram rule of vector addition. For zero vector and arbitrary vector A, there are: 0+A = A+0 = A. | A+B |≤| A |+B |. The addition of vectors satisfies all the laws of addition. The vector with the same length and opposite direction as A is called the inverse quantity of A, -(-a) = A, and the inverse quantity of zero vector is still zero vector. (1) A+(-a) = (-a)+A = 0 (2) A-B = A+(-b). The product of real number λ and vector A is a vector, and this operation is called vector multiplication, and it is denoted as λ a, | λ A | | A |. 0, the direction of λa is the same as that of A, and when λ

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