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high school math theorems centralization
trigonometric formula sheet
basic trigonometric functions with the Kok
the reciprocal relationship: the relationship between business: the square of:
tanα · cotα = 1 ;
sinα · cscα = 1
cosα · secα = 1 sinα / cosα = tanα = secα / cscα
cosα / sinα = cotα = cscα / secα sin2α + cos2α = 1
1 + tan2α = sec2α ;
1 + cot2α = csc2α
(hexagonal Memory Method: Graphic structure \1; shaded triangle trigonometric values of the two vertices is equal to the square of the value under the square of the vertex of the trigonometric functions; any one vertex of the trigonometric function value is equal to the value of two adjacent vertices of the product of trigonometric functions. \
induction formula (formulas: Odd change even the same, Symbols quadrant.)
sin (-α) =- sinα
cos (-α) = cosα tan (-α) =- tanα
cot (-α) =- cotα
sin (π/2-α) = cosα
cos (π/2-α) = sinα
tan (π/2-α) = cotα
cot (π/2-α) = tanα
sin (π / 2 + α) = cosα
cos (π / 2 + α) =- sinα
tan (π / 2 + α) =- cotα
cot (π / 2 + α) =- tanα
sin (π-α) = sinα
cos (π-α) =- cosα
tan (π-α) =- tanα
cot (π-α) =- cotα
sin (π + α) =- sinα
cos (π + α) =- cosα
tan (π + α) = tanα
cot (π + α) = cotα
sin (3π/2-α) =- cosα
cos (3π/2-α) =- sinα
tan (3π/2-α) = cotα
cot (3π / 2-α) = tanα
sin (3π / 2 + α) =- cosα
cos (3π / 2 + α) = sinα
tan (3π / 2 + α) =- cotα
cot (3π / 2 + α) =- tanα
sin (2π-α) =- sinα
cos (2π-α) = cosα
tan (2π- α) =- tanα
cot (2π-α) =- cotα
sin (2kπ + α) = sinα
cos (2kπ + α) = cosα
tan (2kπ + α) = tanα
cot (2kπ + α) = cotα
(where k ∈ Z)
corners and difference of trigonometric functions universal formula for the formula
sin (α + β) = sinαcosβ + cosαsinβ
sin (α-β) = sinαcosβ-cosαsinβ
cos (α + β) = cosαcosβ-sinαsinβ
cos (α- β) = cosαcosβ + sinαsinβ
tanα + tanβ
tan (α + β )=------
1-tanα · tanβ
tanα-tanβ
tan (α-β )=------
1 + tanα · tanβ
2tan (α / 2)
sinα =------
1 + tan2 (α / 2)
1-tan2 (α / 2)
cosα =------
1 + tan2 (α / 2)
2tan (α / 2)
tanα =------
1-tan2 (α / 2)
half-angle of the sine, cosine and tangent trigonometric formulas
descending double angle formula for sine,
团购导航, cosine and tangent triple angle formula for sine, cosine and tangent formula
sin2α = 2sinαcosα
cos2α = cos2α-sin2α = 2cos2α-1 = 1-2sin2α
2tanα
tan2α =-----
1-tan2α
sin3α = 3sinα-4sin3α
cos3α = 4cos3α-3cosα
3tanα- tan3α
tan3α =------
1-3tan2α
difference of trigonometric functions and trigonometric functions of the product formula product of and the difference formula
α + β α-β
sinα + sinβ = 2sin --- · cos ---
2 2
α + β α-β
sinα-sinβ = 2cos --- · sin ---
2 2
α + β α-β
cosα + cosβ = 2cos --- · cos ---
2 2 ;
α + β α-β
cosα-cosβ =- 2sin --- · sin ---
2 2 1
sinα · cosβ =- [sin (α + β) + sin ( α-β)]
2
1
cosα · sinβ =- [sin (α + β)-sin (α-β)]
2
1
cosα · cosβ =- [cos (α + β) + cos (α-β)]
2
1
sinα · sinβ =- - [cos (α + β)-cos (α -β)]
2
of asinα ± bcosα for a corner in the form of a trigonometric functions (trigonometric formulas auxiliary angle
collection, a collection of simple logic functions
any x ∈ A x ∈ B, denoted by A B
AB, BAA = B ;
AB = x ∈ A, and x ∈ B
AB = x ∈ A, or x ∈ B
card (AB) = card (A) + card (B)-card (AB)
(1) the original proposition if the proposition
p q
converse is, if q is any proposition p
if p then q
against any proposition, if q, then p
(2) the relationship between the four propositions
(3) AB, A is a sufficient condition for the establishment of
B BA,
Japan can not afford a small joke - Qzone log, A is a necessary condition for the establishment of B
AB,
Rural economic development ideas - Qzone log, A is a necessary and sufficient conditions for B
function of the nature of the exponential and logarithmic
(1) domain,
上海团购网, range, the corresponding rule
(2) monotonicity
for any x1, x2 ∈ D
if x1 f (x2),
长沙团购网, called f (x) in D is a decreasing function
(3) parity
For a function f (x) within the definition of any one of x,
北京团购网, if f (-x) = f (x), say f (x) is even function
if f (-x) =- f ( x), say f (x) is an odd function
(4) periodic
for the function f (x) within the definition of any one of x, if there exists a constant T, so f (x + T) = f (x), called f (x) is a periodic function (1) Score Index Score Index Power Power
is the significance of the negative fractional index
is the meaning of power
(2) of the nature and number of algorithms
loga (MN) = logaM + logaN
logaMn = nlogaM (n ∈ R) ;
exponential logarithmic functions
(1) y = ax (a> 0, a ≠ 1) is called exponential function
(2) x ∈ R, y> 0
image through the (0,1)
a> 1 时,
Spam Tracking - Qzone log, x> 0,
团购网站大全, y> 1; x 0,0 1
a> 1 时, y = ax is an increasing function of
0 0, a ≠ 1) is called the logarithmic function
(2) x> 0, y ∈ R
image through the (1, 0)
a> 1 时, x> 1, y> 0; 0 1, y 0
a> 1 时, y = logax is an increasing function of
0 0, a ≠ 1)
type with the end of
logaf ( x) = logag (x) f (x) = g (x)> 0 (a> 0, a ≠ 1)
substitution type f (ax) = 0 or f (logax) = 0
series
the basic concepts of arithmetic series, series
(1) general formula of the series an = f (n)
(2) series recurrence formula
(3) series with a general formula of n items and the relationship
an +1- an = d
an = a1 + (n-1) d
a, A, b into the arithmetic 2A = a + b
m + n = k + l am + an = ak + al
common geometric sequence summation formula
an = a1qn_1
a, G, b into a geometric G2 = ab
m + n = k + l aman = akal
inequality
significant inequalities of the basic properties of inequalities
a> bb b, b> ca> c
a> b a + c> b + c
a + b> ca> c-b
a> b, c> d a + c> b + d
a> b, c> 0 ac> bc
a> b, c b> 0, c> d> 0 ac b> 0 dn> bn (n ∈ Z, n> 1)
a> b> 0> (n ∈ Z, n> 1)
(a-b) 2 ≥ 0
a, b ∈ R a2 + b2 ≥ 2ab
| a | - | b | ≤ | a ± b | ≤ | a | + | b |
the basic method of Inequality comparison
(1) to prove the inequality a> b (or a 0 (or a-b 0, to permit a> b, just proved,
to permit a 0, b2 = c2-a2)
eccentricity alignment equation
focus radius | MF1 | = ex0 + a, | MF2 | = ex0-a parabola y2 = 2px (p> 0)
focus F
equation
alignment axis translation
Here (h, k) is the origin of the new coordinate system in the original coordinate system coordinates.
1. Collection of elements with each other hetero######ual ① ② ③ deterministic randomness
2. ① the enumeration method set describeation description of
③ ② ④ Wayne graph the number of axis method
3. Collection operations
⑴ A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
⑵ Cu (A ∩ B) = CuA ∪ CuB
Cu (A ∪ B) = CuA ∩ CuB
4. The nature of the collection
⑴ n element subset of the set number: 2n
subset number: 2n-1; the number of non-empty subset: 2n-2
a summary of high school math concepts, the function
1, if set A has n elements, then set A subset of all the different number is, all non-empty subset of the number is.
quadratic function of the image of the equation is the axis of symmetry, vertex coordinates are. Method of Undetermined Coefficients of the analytic quadratic function, the analytic expression of trying to have three forms, namely, and (vertex type).
2, power function, when n is a positive odd number, m is a positive even number, m 19, the first form by the law of cosines, =
by the law of cosines the second form, cosB =
20, △ ABC, said the area by S, with the circumcircle radius R that with r the radius of the inscribed circle, said that the semi-circumference with p:
①; ②;
③; ④;
⑤; ⑥
21, the projective trigonometry theorem: In △ ABC in,, ...
22, in △ ABC in,, ...
23, in △ ABC in:
;
24, and the plot of the difference formula:
①,
②,
③,
④.
25, and the difference of the product formula:
①,
②,
③,
④.
Third, inverse trigonometric
1, the domain is [-1,1], range is odd function, increasing function;
the domain is [-1 , 1] and a range of non-odd non-even, decreasing function;
the domain is R, range is odd function, increasing function;
The domain is R, range is non-singular non-even, decreasing function.
2, when;
;
for any, there are:
when.
3, the solution set of the simplest trigonometric:
Fourth, inequality
1, if n is a positive odd number, can be introduced by the it? (Can)
even if n is positive it? (Non-negative only when)
2, the same can be subtracted to the inequality, divide up (can not)
can add it? (Can)
can multiply it? (Energy, but conditional)
3, Inequality of two positive numbers is:
three positive numbers mean inequality is:
n a positive mean inequality is:
4, two positive numbers the impaironic mean, geometric mean, arithmetic mean, root mean square is the relationship between the
6, two-way inequality is:
made equal in the time left, the right to obtain equal in time.
five series
1, arithmetic sequence of the general term formula is n items and the former formula is: =.
2, the general term geometric series formula,
ago n items and the formula is:
3, when the geometric sequence of common ratio q satisfy 0, = 0, 0);
sector area formula:;
tapered side expansion plan (sector) of the central angle formula:;
round table side expansion plan (fan ring) of the central angle formula:. through the cone vertex
area of the largest cross-section (cone of bus length, shaft cross-section angle is θ):
XI, the proportion of several properties
1, proportion of basic properties:
2, inverse theorems:
3, more than Theorem:
5, combined ratio theorems;
6, percentage Theorem:
7, combined percentage theorem:
8, division and more than Theorem:
9, geometric theorem: if, then.
second, composite second radical simplification of
When is a completely square, on the shape of the radical reduction using the above formulation is more convenient.
⑵ and set the number of elements:
n (A ∪ B) = nA + nB-n (A ∩ B)
5. N natural numbers or non-negative integers
Z set of integers Q R rational real numbers
6. Simple logic truth table
p consistent with the proposition true and false non-p
false true
II. Function
1. Quadratic function of the pole coordinates:
function vertex coordinates
2. Monotonic function:
in the Department of the extreme value
3. Parity function:
within the definition, if, for the dual function; if was odd function.
1 had two points and only a straight line the shortest line between two points
2
3 of the supplementary angle with the same angle or isometric angle or isometric with
4 The complementary angle equal
5 and only one had a little known straight line and point outside a straight line perpendicular to
6 points connected with straight line segments in all, the vertical section of the parallel axiom
7 after the shortest straight line outside the point, and only a straight line and this line parallel to the
8 If two lines are parallel and the third line, these two lines are parallel to each other
9 Tong Weijiao equal, within two lines parallel to the
10 alternate angles are equal, the two straight lines parallel to the
11 complementary with the adjacent angles, two straight lines parallel to the two parallel
12, Tong Weijiao equal
13 two parallel lines, alternate angles are equal within the two lines parallel
14, complementary with the adjacent interior angles on both sides of the triangle
15 theorems and inference than the third side
16 on both sides of the triangle is less than the third side
17 angles of a triangle and the theorem of the three angles of a triangle is equal to 180 °
18 inferred a right triangle the two acute angles of more than
19 Corollary 2 each triangle and it is not an exterior angle is equal to two adjacent interior angles
20 Corollary 3, a triangle and the exterior angle is greater than any it is not adjacent angles
21 corresponding sides congruent triangles, corresponding angles are equal
22 corner edge axiom (SAS) with the angle between the sides and their corresponding two triangles congruent equal
23 angle corner axiom (ASA) had two horns and their corresponding folders sides congruent two triangles of equal
24 Corollary (AAS) has two horns and one corner of the same on the opposite side of the two triangles congruent corresponding
25 Collage side axioms (SSS) with the corresponding three sides of equal triangles congruent
26 hypotenuse of two right-angled edge of axioms (HL) and a right-angle bevel edge with the corresponding two triangles congruent equal
27, Theorem 1 in the angle bisector of the angle of the point to the same distance on both sides of Theorem 2-1
28 angle from both sides of the same points in the angle bisector of angle
29 to the angle bisector is equidistant from all points on both sides of the set of
30 isosceles triangle isosceles triangle theorem of the nature of the two bottom corners are equal (that is, on the other side isometric)
31 Corollary 1 isosceles triangle The split angle bisectors and perpendicular to the bottom edge of the bottom
32 isosceles triangle the angle bisector, the bottom edge of the middle and the bottom edge of the high overlap each other
33 Corollary 3 of the equilateral triangle angles are equal, and each corner of the isosceles triangle is equal to 60 °
34 Judgement Theorem If a triangle has two angles equal, then the two angles on the sides of the equal (equiangular, equilateral)
35 Corollary 1, three angles are all congruent triangles are equilateral triangles
36 Corollary 2 has an angle equal to 60 ° isosceles triangles are equilateral triangles
37 in a right triangle, if one acute angle equal to 30 ° then it is equal to the hypotenuse of a right-angle side of the half
38 hypotenuse right triangle the hypotenuse is equal to the center line on the half
39 Theorem on the axis line segment point and the two endpoints of this segment
40 inverse and the same distance from a line equidistant from the two end points in this segment of the vertical split line
41 perpendicular bisector of line segment and the segment can be viewed as two end points of all points equidistant Theorem 1 the set
42 symmetrical nearly a straight line shape of the two graphs are identical
43 Theorem 2 If two graphics symmetrical around a straight line, then the corresponding point of the axis of symmetry is perpendicular bisector of the connection
44 Theorem 3, the two graphics on a straight-line symmetry, and if their corresponding intersection line or extension cord, then the intersection of the inverse of the axis of symmetry
45 points if the two corresponding connection graph is a straight line with the axis, then the two graphics on this line symmetry
46 Pythagorean Theorem the two right-angle triangle sides a, b and the square is equal to the square of the hypotenuse c, ie a ^ 2 + b ^ 2 = c ^ 2
47, the converse of the Pythagorean Theorem If the three sides of the triangle long a, b, c has a relationship a ^ 2 + b ^ 2 = c ^ 2, then the triangle is right triangle theorems
48 360 quadrilateral is equal angles and °
49 quadrilateral exterior angle equal to 360 °
50 side polygon-shaped angles and theorems of angles n and is equal to (n-2) × 180 °
-------- -------------------------------------------------- ----------------------
51 deduction equal to any multilateral exterior angle and 360 °
52 parallelogram parallelogram nature of Theorem 1 is equal to the angle
53 parallelogram nature of Theorem 2 on the side of the parallelogram is equal
54 inference caught in between two parallel lines parallel to line the nature of equal
55 parallelogram parallelogram's diagonal theorem 3 to each other equally
56 Parallelogram Theorem 1 determine the two angles are equal to the quadrilateral is a parallelogram parallelogram
57 Theorem 2 to determine the two groups were equal on the side of a quadrilateral is a parallelogram
58 3 diagonal parallelogram decision theorem divide each quadrilateral is a parallelogram parallelogram
59 Theorem 4 to determine a set of parallel sides equal quadrilateral is a parallelogram
60 rectangular nature of Theorem 1, the four corners of the rectangle are right angles
61 rectangular nature of Theorem 2 rectangle to determine the diagonal equal
62 Theorem 1 there are three rectangular angle is right angle of the quadrilateral is a rectangle
63 Theorem 2 to determine the diagonal rectangular parallelogram is a rectangle equal to the diamond nature of Theorem 1
64 diamond The four sides are equal
65 diamond diamond diagonal nature of Theorem 2, perpendicular to each other, and each split a diagonal angle
66 a set of diamond-shaped area = diagonal half of the product, ie S = ( a × b) ÷ 2
67 diamond-shaped sides are equal Theorem 1 determine a quadrilateral is a rhombus diamond
68 Theorem 2 to determine the diagonal of the parallelogram are perpendicular to each other diamond properties
69 square four-square theorem 1 corners are right angles, four sides are equal
70 square nature of Theorem 2, the two diagonal squares are equal, and perpendicular to each other equally, and each split a set of diagonal angle on the center of Theorem 1
71 symmetry of the two graphs are congruent
72 Theorem 2 on the center of symmetry of the two graphs, symmetric connection points have been the center of symmetry, and is inverse symmetry split
73 points if the two corresponding graphic connections have been a point, and is it equally, then the two graphics on this point the nature of symmetry
74 isosceles trapezoid isosceles trapezoid theorems in the same bottom two corners on the isosceles trapezoid are equal
75 The two diagonals are equal decision theorem
76 isosceles trapezoid in the same two corners on the bottom of the ladder are equal isosceles trapezoid
77 diagonal trapezoid is isosceles trapezoid equal parallel
78 Equal line segment Theorem If a group of parallel lines cut in a straight line segment obtained
equal, then the other straight line intercepted the line are equal
79 Corollary 1, the midpoint of the waist through the ladder and at the end of a parallel a straight line, will split the other after lumbar
80 Corollary 2 the midpoint of the triangle and the other side of the side parallel to the line, will split the third side
81 Theorem triangle median line median line of the triangle parallel to the third edge, and is equal to half of it
82 trapezoid trapezoid theorem of the median line median line parallel to the two end and two equal to half of the bottom and L = (a + b) ÷ 2 S = L × h
83 (1) If the proportion of the basic properties of a: b = c: d, then ad = bc
if ad = bc, then a: b = c: d wc / S?
84 (2) If the nature of cooperation than a / b = c / d, then (a ± b) / b = (c ± d) / d
85 (3) geometric properties if a / b = c / d = ... = m / n (b + d + ... + n ≠ 0), then
(a + c + ... + m) / (b + d + ... + n) = a / b
86 sub-segments of parallel lines is proportional to the three theorems two parallel lines cut straight line obtained is proportional to the corresponding inference
87 line parallel to the cut-off the other side of the triangle on both sides (or both sides of the extension cord), which is proportional to the corresponding segment
88 Theorem If a line cut both sides of the triangle (or both sides of the extension cord) from the corresponding line segments proportional, then this line parallel to the triangle's third side
89 parallel to the side of the triangle, and the other on both sides of the intersection of the straight line obtained by the cut-off triangular with the original triangle is proportional to the corresponding sides of a triangle parallel to the triangle
90 theorems and other side of the line on both sides (or both sides of the extension line) intersects the triangle composed of the original triangles similar triangles to determine similar
91 Theorem 1 equal to the corresponding corners of two triangles similar to the (ASA)
92 high on the hypotenuse of a right triangle is divided into the two triangles and a triangle similar to the original decision theorem 2
93 proportional to the corresponding sides and angles equal The two triangles similar to the (SAS)
94 Theorem 3 to determine the corresponding three sides in proportion to the two triangles similar to the (SSS)
95 Theorem If the hypotenuse of a right triangle and a right angle with another side of the hypotenuse and a right-angle side of the corresponding proportion, then the two triangles similar to the properties of Theorem 1
96 higher than the corresponding similar triangles, corresponding to the center line than the corresponding angle bisector and the ratio is equal to the theorem of similar nature than
97 2 similar triangles is equal to the ratio of the circumference of similar nature than
98 area of a triangle similar to Theorem 3 ratio is equal to the square of
99 similar than the sine of any acute angle is equal to the cosine of its complementary angle, the cosine of any acute angle equal to its complementary angle of the sine
100 tangent of any acute angle equal to its complementary angle of the cotangent value of the contingent value of any acute angle equal to its complementary angle tangent
--- -------------------------------------------------- ---------------------------
101 round is a distance equal to the fixed-length fixed-point set of points
102 inside the circle can be seen as the distance is less than the radius of the center set of points outside the circle
103 can be seen as the distance is greater than the radius of the center point of the set
104 round or so with the same radius of the circle
105 a distance equal to the fixed point of the trajectory length, is the point of a circle, a circle of radius length and known
106 segments of equal distance from both end points of the track, is the section perpendicular bisector of the line segment to a known angle
107 equidistant points on both sides of the track, is the angle bisector of two parallel lines
108 到 locus of points equidistant, and it is two parallel lines parallel and equidistant Theorem is not a straight line
109 three-point line has been established with a circle.
110 vertical diameter perpendicular to the chord of the diameter of Theorem equally split this string by string and the two arcs
111 of Corollary 1 ① split string (not diameter) of the diameter perpendicular to the strings, and split the right chord arc
② two perpendicular bisector of string through the center of the circle, and the strings are split on the two arcs
③ split the string on the diameter of an arc, vertical split string, and split the string by another pair Corollary 2 arc
112 round clip of two parallel strings are equal
113 circle arc is the center of the center as the center of symmetry theorem of symmetry
114 round or so in the same circle, equal central angle The equivalent of the arc, the equivalent of the string, the string on the heart strings of inferences from the same
115 round or so in the same round, if the two central angle, two arcs, two string or two strings heart strings in a set amount of distance equal to that they correspond to the amount of the other groups are equal
116 theorem of an arc on the circumference of the angle of the central angle is equal to its half
117 Corollary 1 with the arc or other arc of the circumference of the equal angles; the same circle or other circular, the equivalent of the circumferential angle of the arc are equal
118 Corollary 2 semicircle (or diameter) of the circumferential angle of a right angle; 90 ° of the circumferential angle The diameter of the string is
119 Corollary 3 If the center line on the side of the triangle is equal to half the side, then the triangle is right triangle within the circle theorems
120 quadrilateral diagonal complementary, and any exterior angle is is equal to its angle within
121 ① ⊙ O line L and intersects d r?
After 122 Tangent Theorem to determine the radius of the outer end and perpendicular to the radius of this circle tangent line is tangent to the nature of the Theorem
123 round after a cut perpendicular to the tangent point of the radius of the
124 1 through the center of the circle and the inference will be perpendicular to the tangent line through the tangent point
125 Corollary 2 points after a cut perpendicular to the tangent line through the center
126 will be a long tangent point theorems introduced from outside the circle of the two tangent circles, their appearance and so the tangent , center, and split the connection that the angle between two tangents
127 quadrilateral circumscribed circle on the side of the two groups and equal
128 Xian Qiejiao Theorem Xian Qiejiao arc is equal to its folder The circumferential angle
129 deduction if both the folder Xian Qiejiao arc equal, then the two are equal
130 Xian Qiejiao intersection of the two strings intersect circle theorem of string, was divided into two intersection equal to the product of a long line
131 deduction if the strings with the diameter of vertical intersection, then the string by half its diameter into two sub-segments in the proportion of Theorem cutting line item
132 point lead from outside the circle tangent to the circle and the secant, tangent length is that the secant and the circle to the intersection point of two line segments in the proportion of long-term
133 inferences that lead from outside the circle round the two secant, which is the secant and the circle of each the intersection of the product of two equal length segments if the two circles tangent
134, then the cutoff point must be in line with the heart outside the two circles
135 ① from the d> R + r ② d = exterior of two circles R + r
③ two circles intersect Rr r)
④ two circles inscribed d = Rr (R> r) ⑤ two circles containing d r)
136 theorems with the two circles intersect the axis center line of two circles of the public * String
137 into the circle theorem of n (n ≥ 3):
⑴ points followed by links from each polygon is The circle inscribed n-gon
⑵ points for each round after the tangent to the intersection of the tangent to the adjacent vertices of this polygon is a circle circumscribed n-gon theorem of any regular polygon
138 has a circumcircle and an inscribed circle, the two circles are concentric
139 regular n-gon of each interior angle is equal to (n-2) × 180 ° / n
140 theorems are n edge radius and the shape of the heart from the positive side of n-gon is divided into 2n congruent right triangle
141 a n-gon is the area of Sn = pnrn / 2 p n-gon that is the perimeter of an equilateral triangle
142 area of √ 3a / 4 a side
143 that if a vertex k-regular nearly the corner n-gon, and these angles should be 360 °, so k × (n-2) 180 ° / n = 360 ° into the (n-2) (k-2) = 4
144 arc length formula: L = n Wu R/180
145 fan-shaped area formula: S fan = n Wu R ^ 2 / 360 = LR / 2
146 within the common tangent length = d-(Rr) grandfather tangent length = d-(R + r)
multiplication and causeing
a ^ 2-b ^ 2 = ( a + b) (ab)
a ^ 3 + b ^ 3 = (a + b) (a ^ 2-ab + b ^ 2)?
a ^ 3-b ^ 3 = (ab (a ^ 2 + ab + b ^ 2)
triangle inequality | a + b | ≤ | a | + | b | | ab | ≤ | a | + | b | | a | ≤ b -b ≤ a ≤ b
| ab | ≥ | a | - | b | - | a | ≤ a ≤ | a |
the solution of a quadratic equation-b + √ (b ^ 2-4ac) / 2a-b - √ (b ^ 2-4ac) / 2a
relationship between roots and coefficients X1 + X2 =- b / a X1 * X2 = c / a Note: Whyte Theorem
discriminant
b ^ 2 -4ac = 0 Note: The equation has two equal real roots
b ^ 2-4ac> 0 Note: The equation has two unequal real roots
b ^ 2-4ac <0 Note: The equation has no real roots, complex roots are conjugate trigonometric formulas
corners and formulas
sin (A + B) = sinAcosB + cosAsinB
sin (AB) = sinAcosB-sinBcosA
cos (A + B) = cosAcosB-sinAsinB
cos (AB) = cosAcosB + sinAsinB
tan (A + B) = (tanA + tanB) / (1-tanAtanB)
tan (AB) = ( tanA-tanB) / (1 + tanAtanB)
cot (A + B) = (cotAcotB-1) / (cotB + cotA)
cot (AB) = (cotAcotB +1) / (cotB-cotA )
chi flat irons Born deaf and mute girl speak after
Hybrid Mode
