The polar coordinate equation of a straight line passing through a point with an inclination angle is: 14. Two straight lines are parallel, and the angle formula of 8 or 3 times is: sin3=cos3= 1-3tan2α. If a point is a point on a parabola, the distance from the point to the focus of the parabola (called focal radius) is:, and a chord passing through the focus of the parabola and perpendicular to the axis of symmetry of the parabola (called path). Tan(3π/22. Set Representation ① Enumeration ② Description COS3α = 4cos3α-3cosα1-tan α-tan β (1) Definition domain, range and corresponding rules ⑤; ⑥ sin (2kπ+α) = sinα cot (π/2-α) = tanα. On the domain of definition, if, it is an even function; If so, odd function. There is only one straight line and one known straight line in the vertical sequence of 38 right-angled triangles. The median line on the hypotenuse is equal to half of the hypotenuse. (3) A B, and A is the sufficient condition for B. 2 The shortest line segment between two points is 24 Inference (aas) Two triangles have two angles and the opposite sides of one angle are congruent. 2 2 15 theorem The sum of two sides of a triangle is greater than the third side. Number of subsets of (1)n element set: 2ntan (π/2-α). In 1, x>0, y> 1; x0，0 1a & gt； When 1, y=ax is increasing function cos(α+β)=cosαcosβ-sinαsinβ point skew formula:, skew formula: the complementary angles of three identical angles or equal angles are equal. If points p 1, p2 and p are points on a straight line, their corresponding parameters in the above parameter equation are: when point p is divided into directed line segments,; When point p is the midpoint of line segment p 1p2, 1. Establish a rectangular coordinate system with the vertex of the angle as the coordinate origin and the starting edge as the positive semi-axis of the X axis. Take any point different from the origin on the last side of the angle, and record the distance from point P to the origin as sin=, cos=, tg=, ctg=, sec=, csc=. 4. Demovo's theorem is: directrix equation 5. If point and point P divide the directed line segment into a fixed ratio λ, then λ = =; The hyperbolic equations of the image passing through (1, 0)22 and hyperbolic * * * asymptotes are as follows. Hyperbolic equations with hyperbola as the focus are. Inference 1 A triangle with three equal angles is an equilateral triangle 1. Set elements have ① certainty ② mutual anisotropy ③ The included angle θ between disordered lines satisfies: the equation of symmetry axis of the image of quadratic function is, and the vertex coordinates are. When using the undetermined coefficient method to find the analytic expression of quadratic function, there are three methods to find the analytic expression, namely sum (vertex). 3. Binomial Theorem: The general formula of binomial expansion: 9. Distance from point to straight line: from the second form of cosine theorem, cosb=cos()cos()=. A b, A is B's necessary and sufficient condition Card (A b) = Card (A)+ Card (B)- Card (A b) (where k∈z) 1+cot2α=csc2α5, the polar coordinate equation of a circle with the center at the pole and the radius r is; The equation of the line system passing through the intersection of two straight lines is: 3. Inverse trigonometric function COS α sin β =-[SIN (α+β)-SIN (α-β)] 2. When; The average inequality of n positive numbers is: 7. Several forms of linear equation: 17, trigonometric function value of special angle: tan(3π/2+α)=-cotα Summary of senior high school mathematics concepts 20. △ The area of △abc is represented by S, the radius of circumscribed circle is represented by R, the radius of inscribed circle is represented by R, and the half circumference is represented by P: the increasing interval of COSα-COSβ= is, and the decreasing interval is; The increasing interval of is, the decreasing interval is, the increasing interval is, and the decreasing interval is. (1) Proposition What is the special relationship between the distribution of their corresponding points on the complex plane? Can you multiply? (Yes, but with conditions) The basic relationship of trigonometric functions with the same angle XII. Simplification of compound quadratic root 2 12. Can the same inequality be subtracted and divided? (No) 3. Solution set of the simplest trigonometric equation: if the original proposition is p, then q takes the extreme value. 6. Two-way inequality is: 3. Comparison theorem: 3. Wayne chart 4. Number axis method 5. Vertex coordinates of sequence functions are among them. P is not p υ Cu (a ∩ b) = cua ∪ cubcu (a ∪ b) = cua ∪ cub4. The properties of a set are lateral area of a regular pyramid and lateral area of a regular prism. There are three possible cases for the trajectory of tan(2kπ+α)=tanα⑥: a) The trajectory at that time was hyperbola; B) The trajectory at that time was two rays; C) At that time, the trajectory did not exist. The meaning of negative fractional exponential power is (2)x∈r, y>0 (1) y = ax (a > 0, a≠ 1) is called the exponential function tg===. 2 17, the angle doubling formula is: sin2=4, the polar coordinate equation of the line crossing the pole and having an inclination angle is: 0,4, the lateral area definition domain is r, and the range is odd function and increasing function; Theorem 39 The distance between the point on the vertical line of a line segment and the two endpoints of the line segment is equal to ①; ②; 1 1, the power decreasing formula is: the polar coordinate equation of the straight line passing through this point and perpendicular to the polar axis is: 3. Volume formula: a> in 1, x> 1, y>0; 0 1, y0 a> when 1, y=logax is increasing function VIII. Analytic geometry 37 in a right triangle, if an acute angle is equal to 30, then the right side it faces is equal to half of the hypotenuse. Arithmetic progression's basic concepts. Polar coordinates, parameter equation 2. Monotonicity of functions: cone:, cone:. ③ There is only one straight line 00 at the intersection of1. A ≠ 1) is called logarithmic function 22. At △abc, … exponential function logarithmic function cos (π/2+α) =-sin α1+tan 2 (α/2) angle 29 bisector. Cos (2kπ+α) = cos α cot (-α) =-cot α =. cos (π/2-α) = sin α. The formula of the central angle of the frustum of a cone (sector ring) is: when it is a complete square number, it is more convenient to simplify the radical with the above formula. Cot(3π/2+α)=-tanαα+βα-β② Investigate the relationship between the distance to the center of the circle and the radius: the distance is greater than the radius, equal to the radius, and less than the radius, which is equivalent to the separation, tangency and intersection of straight lines and circles. 5. Several basic formulas: 3. The triangle inequality in the complex set is:, where the vector lines corresponding to complex numbers z 1 and z2 are inverted (in the same direction), and the left side is equal, while the vector lines corresponding to complex numbers z 1 and z2 are inverted (in the same direction). Formulas of trigonometric functions. If the equation of a circle with the diameter of line segment ab is 3. If a polar coordinate system is established, with the origin of the rectangular coordinate system as the pole, the positive semi-axis of the X axis as the polar axis, and the polar coordinate of the P point as the rectangular coordinate, then the judgment theorem of …34 isosceles triangle If a triangle has two equal angles, the opposite sides of the two angles are also equal (equilateral). 2. Inverse ratio theorem: 25. Sum product formula: trigonometric function and product formula tan (2 π-α) =-tan α (1) a ∩ (b ∪ c) = (a ∪ b) ∩. secαsin 2α+cos 2α= 1 1+tan 2α= sec 2αII。 Function cos(α-β)=cosαcosβ+sinαsinβ Combination Number Properties: =+=5, Combination Theorem; (2)x & gt； 0，y∈ra & gt； B>0 & gt(n∈z, n> 1) Thinking: What kind of figure does the equation represent when summing? The focal radius |mf 1|=ex0+a, |mf2|=ex0-a parabola y2=2px(p 0)tanα+tanβ true and false 22 1 sin α cos β =-[sin (α+β)+sin (α-β)] 27 theorem. Binomial Theorem 20 infers that an outer angle of a triangle is greater than any inner angle that is not adjacent to it (00, a≠ 1). The polar coordinate equation of a straight line passing through a point and parallel to the polar axis is: if the negative proposition is Q, then P (hexagonal memory method: the graphic structure is "the upper chord is cut, and the Zuo Zheng is1"; The product of two functions on the diagonal is1; The sum of squares of trigonometric function values of two vertices on the shadow triangle is equal to the square of trigonometric function value of the next vertex; The trigonometric function value of any vertex is equal to the product of the trigonometric function values of two adjacent vertices. " ) The average inequality of three positive numbers is: 1 1. The standard equation of a circle is: 2 2 The equation of a circle passing through the intersection of a straight line and a circle is: What if n is a positive even number? (Only when they are all non-negative) For any x 1, x2∈d 10, the distance between two parallel straight lines is (4) period 0SIN0 10If f(-x)=-f(x), and f(x) is called odd function (2 3 1 Inference 1 The bisector of the vertex of an isosceles triangle bisects the base and the domain perpendicular to the base is r, and the range is odd or even, which is a negative function. ⑤ There may be three cases of trajectory: a) The trajectory was elliptical at that time; B) The trajectory at that time was a line segment; C) At that time, the trajectory did not exist. How to calculate the property index and logarithm of the function 1 (first find the remainder obtained by dividing n by 4. The formula of α+β α-β combination number is: = =; The sum formula of the first n terms of sin(-α)=-sinα is: 24. The geometric meaning of the focal point parameter p of conic curve is the distance from the focal point to the directrix, which is true for both ellipse and hyperbola. The trajectory of false truth ② is a ray. 24. sum and difference formula of products: cos (-α) = cos α tan (-α) =-tan α13, sin()sin()=, if so, the coordinates of the center of gravity g of △abc are. 2. The general formula of geometric series is: the definition domain of 1 is [- 1, 1], and the value domain is, odd function and increasing function; 1-tan2α sin α sin β =-[cos (α+β)-cos (α-β)]16 infers the basic property that the difference between two sides of a triangle is less than the third side inequality. Important inequality tan2α=-25, translate the coordinate axis so that the coordinate of the origin of the new coordinate system in the original coordinate system is (h, k). Two-point formula: intercept formula: tan α =-5, arithmetic progression, if sn= 10 and s2n=30, then s3n = 60 coordinate axis translation cot(π-α)=-cotα4 with the same angle or the same complementary angle is equal; (2) monotonicity is 10, and the formula for raising power is: 1. If there are n elements in set A, the number of all different subsets of set A is, and the number of all non-empty proper subset is. Cos(3π/2+α)=sinα inequality tg2=. The domain of is [- 1, 1], and the range of values is, odd or even, negative function; The general equation of any circle is: (2) Number of union elements:13; General term formula of sequence with equal dislocation angles in parallel lines (1); An=f(n) the formula of the central angle of the cone-side development diagram (sector); ① Discrimination method: δ0, = 0,0, which is equivalent to the intersection, tangency and separation of a straight line and a circle; The division relation is:,. (1) The trajectory is a ray. Proper subset number: 2n-1; Non-empty proper subset number: 2n-2 Eccentricity COS (π+α) =-COS α 211is complementary to the inside angle, two straight lines are parallel to 16, the focal coordinate of parabola is:, and the directrix equation is:. The maximum cross-sectional area of α+β α-β passing through the apex of the cone is (the length of the generatrix of the cone is, and the vertex angle of the shaft section is θ): they are all located on a circle with the center of the circle as the origin and the radius, and divide this circle into n equal parts. Compare the sum of the general term formula of the equation COS (3 π/2-α) =-SIN α sin (3 π/2+α) =-COS α (3) and the first n terms COS 2 α = COS 2 α-SIN 2 α = 2 COS 2 α-1-2 SIN 2 α 65438. Cylinder:, cylinder:. Inference 3 All angles of an equilateral triangle are equal, and each angle is equal to 60 7. Divisibility ratio theorem: sin(π+α)=-sinα 13, and the tangent equation with the circle as the tangent point is 8. If two straight lines are parallel to the third straight line, they are also parallel to each other. Tg 0 1 does not exist. (2) The recurrence formula of series does not exist. One of them is. Cos 10 0 1, the projective formula of dihedral angle is, where the meanings of each symbol are: the area of figure f on one plane of dihedral angle, the projection of figure f on another plane of dihedral angle, and the size of dihedral angle. 23. If the straight line intersects the conic curve at two points A (X 1, Y 1) and B (X2, Y2), the chord length is; sin(π-α)= sinαtan(π-α)=-tanαwhen。 The commonly used summation formula 9 of geometric progression with any x∈a x∈b labeled a B. Cos(2π-α)=cosα is the same as the complementary angle, and two lines are parallel to COT (2π-α) =-COT α = Z Integer Set Q Rational Number Set R Real Number Set ③ The trajectory is a circle. ④。 4. If point P divides the directed line segment into constant ratio λ, λ =

3. The approximate image of the function is 1, the general term formula of arithmetic progression is, and the sum formula of the first n terms is: =. The dislocation angles in 10 are equal, and two straight lines are parallel. Tan (π/2+α) =-COT α = α+β α-β A > b bb，b & gtc a & gtc a & gtb a+c & gt； b+ c a+b & gt； c a & gtc-b a & gtb，c & gtd a+c & gt； b+ d a & gt； b，c & gt0ac & gt； BC a>b, cb>0, c>d>0 acb & gt0dn & gt；; Bn(n∈z, n> 1) converts asinα bcosα into an angle trigonometric function (formula ③ of auxiliary angle trigonometric function; ④; Formula of trigonometric function A set of simple logic general formula for sum and difference of two angles 3. The inductive formula can be summed up in ten words: odd change couples, symbols look at quadrants. For example =,. Sin(π/2-α)=cosα sector area formula: The hyperbolic standard equation has two forms: SUMCOT (π/2+α) =-TAN α COT (3 π/2-α) = TAN α-TAN β 3 TAN α-TAN 3 α1,and Schell formula: SIN 3 α = Then f(x) is said to be the fifth power (1) of the fractional exponent of the periodic function. If it is not a zero complex number, then z has n square roots, namely: arc length formula: (it is the radian number of the central angle, 0); Theorem 2 of parity 28 of homomorphism type (3) reaches a point where both sides of an angle are equidistant. From the bisector of this angle, the range of the function is, the monotone increasing interval is, and the monotone decreasing interval is. The property theorem that the corresponding edges and angles of 2 1 congruent triangles are equal to 30 isosceles triangles. The sine, cosine and tangent formulas of the two base angles of an isosceles triangle are equal (that is, equilateral and equiangular). The power formula of trigonometric function is the sine, cosine and tangent formula of double angle. The sine, cosine and tangent formulas of triple angle are 23. At △abc: 12. Two lines are parallel and the congruence angle is equal to SIN (. A b={x|x∈a, or x∈b} Comparison method 1+tan α tan β 6 Of all the line segments connected with points, the shortest vertical line segment is 2tan(α/2) XI. Some properties of the ratio | A |-| B | ≤| A B When the series is geometric series, there are. 3. The parameter equation of a circle with the center at point and radius is: ②, sin(2π-α)=-sinα 19. If a point is a point on an ellipse and is its left and right focus, then the length of the focal radius of point P is sum. 1. If n is a positive odd number, can it be deduced from? (energy) 2. Power function, when n is a positive odd number, m is a positive even number, and m n, its approximate image is 2tanα 14, =; Inductive formula (formula: odd variable couple, sign according to quadrant. ) sphere:. 6. In geometric series, if Sn = 10 and S2N = 30, then S3n = 70cos2 = = equals sign when the left side exists, and equals sign when the right side exists. 8. Switch ratio theorem: 15. The four forms of parabolic standard equation are: the basic method of proving inequality 4. The maximum value of the function is, the minimum value is, the period is, the frequency is, the phase is, and the initial phase is; The symmetry axis of the image is a straight line, and the intersection of the image and the straight line is the symmetry center of the image. Second, the trigonometric function tan (α-β) =-2. If a straight line passes through a point, the standard form of the straight line parameter equation is: the geometric meaning of the parameter t corresponding to point P is: the number of directed line segments. Sinα= - 6。 The relationship between the number of complex numbers and the number of combinations is: where the radius is, the central coordinate is 17, and the sum of the three internal angles of the theorem triangle is equal to 180, then the included angle θ between straight lines satisfies: generally, the tangent equation with a curve as the tangent point is: for example, the tangent equation of a parabola with a point as the tangent point is:, that is:. (1) Prove the inequality A >: B (or a0 (or a-b0, to prove a>b, you only need to prove that the image passes (0, 1)2. In the relationship of trigonometric functions with the same angle, the square relationship is:,,; =6. In simple logic, if Q and p36 infer that an isosceles triangle with an angle equal to 60 is an equilateral triangle ③, cos α cos β =-[cos (α+β)+cos (α-β)]1-tan 2 (α/2) 4, two positive numbers. What are the characteristics? (a-b)2≥0 a，b∈r a2+b2≥2ab3。 Operation of set 7, =. (2) The relationship between the four propositions. Note: this conclusion can only be used to do multiple-choice questions or fill-in-the-blank questions. If it is a solution, it can only be done according to the routine process of finding the tangent equation. 2 1, the projective theorem in trigonometry: in △abc, … 1. Polar coordinates of quadratic function: sin(α+β)=sinαcosβ+cosαsinβ2, and the distance formula between two points on the number axis: logaf (x) = logag (x) f (x) = g.0 (a > 0，a≠ 1)6。 If points m and n are selected, then. 9. Equal proportion theorem: If, then. The axiom of edges and corners (sas) has two triangles with equal angles. Congruent COS α =-loga (Mn) = logam+logan logam = nlogam (n ∈ r) The included angle θ between straight lines satisfies: tan α cotα =1sin α CSC α = 65438+. Generally speaking, if the limit of the sum of the first n terms of an infinite series exists, it is called the sum of the terms of this series (or the sum of all terms), which is expressed by S, that is, s=. Cot(π+α)=cotα 14。 There are two most commonly used methods to study the positional relationship between a circle and a straight line, namely, the lateral area of a cylinder; The lateral area of the cone; 9. The half-angle formula is: sin=cos=2 1, and the classes are independent; Multiplication is step by step, step by step correlation. A b, b aa=b ab={x|x∈a, x∈b} Reciprocal relation: quotient relation: square relation: 6. If the points corresponding to the complex numbers z 1 and z2 are a and b, respectively, then the area of △aob(o is the coordinate origin) is. B a, A is the necessary condition for B to be established =; 6. Fractional theorem: Seven parallel axioms pass through a point outside a straight line. There is only one straight line parallel to this straight line. 17. The two forms of elliptic standard equation are: and if there are two circles, there is no proposition, and if p is q, the mathematical formula theorem in high school is concentrated. The basic nature of the ratio of 1. has been determined. Function 18 Inference 1 Exponential power of the mutual JUNG WOO fraction of two acute angles of a right triangle means that 19 Inference 2 An outer angle of a triangle is equal to the sum of two non-adjacent inner angles, and sin(α-β)=sinαcosβ-cosαsinβ25-sided axiom (sss) has two triangles and three corresponding ones at one point. 16, sin 180= .2. If the projection of a straight line on the plane is a straight line, and the straight line M is a straight line passing through the inclined foot on the plane, the angle it forms is, and the angle it forms is θ, then the relationship between these three angles is. 4. Inequality 8. Several basic trajectories of points corresponding to the complex number Z in the complex plane: an+1-an = Dan = a1+(n-1) d a, a and b are equal to 2A = A+B M+N = K+L AM+An = AK. (energy) 3. The average inequality of two positive numbers is: the equation of the circle system at the intersection is: 3. The parity of the function is: an = a 1qn _ 1A, the ratio of g to b is g2=ab m+n=k+l aman=akal 12, and the universal formula is SIN. Sinα+sinβ = 2sin-cos-6,8, straight line, then the included angle θ between straight line and straight line satisfies: the general formula of focus F: ctg does not exist 1 0 does not exist 0 18, and the sine theorem is (where R represents the radius of the circumscribed circle of a triangle): 2tan (α/2) tan (./). 3. The distance formula between two points on the rectangular coordinate plane: X. Solid geometry sin α-sin β = 2cos-sin-26 Axiom of hypotenuse and right angle (hl) The volumes of the right triangle corresponding to two hypotenuse and a right angle are equal: (where, it is the straight section area and the side length); Reciprocal relationships are:,,; Sin (π/2+α) = cos α 22n (A ∪ B) = Na+Nb-N (A ∪ B) lateral area of a straight prism:, lateral area of an oblique prism:; 2. Are the two imaginary cubic roots of 1, and: The polar coordinate equation of the circle whose center is at point is; Here's a little. I don't know which one you want. Choose for yourself.