文档介绍：该【重要数学公式（Importantmathematicalformula） 】是由【蓝天】上传分享，文档一共【9】页，该文档可以免费在线阅读，需要了解更多关于【重要数学公式（Importantmathematicalformula） 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。重要数学公式(Important mathematical formula)
The 95 theorem, if the right side of a right triangle and the right angle are three right angles
The corner of the corner is proportional to a right angle, so the two right triangles are similar
property theorem 1, the ratio of the corresponding triangle, the ratio of the corresponding line and the corresponding angle flat
The ratio of the line to line is equal to the similitude ratio
property theorem 2 the ratio of the perimeter of a similar triangle is equal to the ratio of the similarity
property theorem 3 the ratio of the area of a similar triangle is equal to the square of the similarity ratio
sine random acute value equal to its angle cosine value, the cosine value of arbitrary angle
It is the complement of the value in the sine
Tangent 100 any acute angle value equal to its complement of the cotangent value, the value of any angle.
It is tangent to the value angle
The 101 circle is the set of points whose distance is equal to the fixed length
The inner part of a 102 circle can be regarded as a set of points whose distance is smaller than the radius
The outer part of a 103 circle can be regarded as a set of points whose distance is greater than the radius
With 104 or so is equal to the radius of the circle
The distance from 105 to the point is equal to the locus of the fixed point. The point is the center of the circle and the length is half
Diameter circle
The trajectory of a point equal to the distance between two endpoints of a known line segment, is the vertical of a line segment 106
Bisector
The trajectory of a point equal to the distance between 107 sides of a known angle: the bisector of this angle
The trajectory of points from 108 to two parallel lines that are parallel and equidistant from the two parallel lines
A line that is equal
The 109 theorem does not determine a circle at three points on the same line.
the vertical diameter theorem is perpendicular to the diameter of the chord, equal to the string, and the two arcs of the string are equally divided
deduction 1. The diameter of the chord (not diameter) is perpendicular to the string and the two arcs of the string are equally divided
The vertical bisector of the chord passes through the center of the circle and divides the two arcs of the string equally
Equal to the diameter of an arc to which the chord is right, vertically equal to the chord, and equal to the other arc of the string
infer that the arc of the two parallel strings of the 2 circle is equal
The 113 circle is a central symmetrical figure centered on the center of the circle
114 theorems in the same circle or congruent circles, arc equal central angle of the chords.
Equal, the chord of the pair of strings has equal center distance
In the 115 round or round deduction, if the two central angle, two arcs, two strings or two
There is a set of equal distances in the chord spacing of strings, and the rest of them are equal
The 116 theorem, the circumference of a pair of arcs is equal to half the angle of the center of the circle it is centered on
corollary 1 with arc or arc on the circle with equal angles : or circle, equal circumferential angle of the arc are equal
infer that the circumferential angle of the 2 semicircle (or diameter) is right angle, and the circumferential angle of 90 degrees is
The right chord is the diameter
inference 3 if the center line on one side of the triangle equals half of the side then the triangle is a right triangle
Complementary diagonal inscribed quadrilateral 120 circle theorem, and any one corner is equal to it
Inner diagonal
lines L and 0 intersect, d < R
The L and 0 / d=r tangent line
The linear L and 0 from D / > R
the judgment theorem of tangents follows the outer edge of the radius and the straight line perpendicular to the radius is the tangent of the circle
the nature of the tangent theorem; the tangent of the circle is perpendicular to the radius of the tangent point
inference 1 the straight line passing through the center of the circle and perpendicular to the tangent must pass through the point of tangency
inference 2 the straight line passing through the point of tangency and perpendicular to the tangent must pass through the center of the circle
the long tangent theorem, the two tangents of a circle from a point outside the circle, whose tangents are equal,
The line between the center of the circle and this point divides the angle between the two tangents
The two sets of 127 sides of a circumscribed quadrilateral and equal
The 128 angle is equal to the circumference of the clamping angle theorem of arc angle
that if the two angle between the arc are equal, then the two angle is equal
intersecting strings, the two intersecting strings in a circle, the product of two lines separated by intersection
points
Equal
it is deduced that if the chord is perpendicular to the diameter, then half of the string is divided by its diameter
Two line mean proportional
cutting line theorem, the tangent and secant of a circle from a point outside the circle, and the tangent length is from this point to the cut
The two lines long line and circle intersection mean proportional
the two secant of a circle from a point outside the circle, which is equal to the product of the length of each of the two segments of the intersection of the Secant and the circle
If the two circles are tangent, then the point of tangency must be on the center line
135, two, D, R+r, two circles, d=R+r
The two circles intersect with R-r < d < R+r (R > R)
Two circle inscribed d=R-r (R > R). The two circle contains d < R-r (R > R)
A common chord in which 136 lines of two intersecting circles are vertically divided into two equal circles
Divide the circle into 137 theorems of n (n = 3):
The connecting points of the polygon in turn is the circle inscribed regular n polygon.
After all the points are tangent to a circle, the intersection adjacent vertex tangent polygon is the circle tangent regular n polygon.
138 any theorem polygon has a circumscribed circle and a circle, these two circles are concentric
Each corner 139 regular n polygon is equal to (n-2) * 180 degrees / n
The 140 theorem is the radius and the edge distance of the positive n edge. The positive n edge is divided into 2n congruent right triangle
141, the area of the positive n edge is Sn=pnrn / 2 P, which represents the perimeter of the positive n edge
The 142 is the triangle area root 3A / 4 a side said
143 If there is an angle of K positive n edges around a vertex, the sum due to these angles should be
360 degrees, therefore, K * (n-2) 180 deg / n=360 degrees is (n-2) (K-2) =4
The 144 arc length formula: L=n was R / 180
The 145 sector area formula: S sector =n Wu R"2 / 360-LR / 2
146 inside cut line = d- (R-r) grandfather tangent length = d- (R+r)
(there are some others.)
Utilities: common mathematical formulas
Formula, formula, formula, expression
Multiplication and factor, a2~b2= (a+b) (a~b), a3+b3= (a+b) (a2_ab+b2), a3_b3= (a_b (a2+ab+b2))
The triangle inequality is less than or equal to a|+|b less than or equal to |a|+|b| |a~b a+b |a = b<=>-b = a = b
a~b| = a|-|b -|a = a = a
-b+ have the solutions of quadratic equation with one unknown of the (b2-4ac) /2a -b- (b2~4ac) /2a V
Relation between roots and coefficients Xl+X2=-b/a, Xl*X2=c/a notes: the laws of Weber
Discriminant
B2-4ac=0 note: equations have two equal real roots
B2~4ac>0 note: the equation has two unequal real roots
B2~4ac<0 note: the equation has no real roots and has conjugate complex roots
Trigonometric function formula
The horns and formula
Sin (A+B) =sinAcosB+cosAsinB sin (A-B) =sinAcosB-sinBcosA
Cos (A+B) =cosAcosB-sinAsinB cos (A-B) =cosAcosB+sinAsinB
Tan (A+B) = (tanA+tanB) / (1-tanAtanB) Tan (A-B) = (tanA-tanB) / (1+tanAtanB)
CTG (A+B) = (ctgActgB-1) / (ctgB+ctgA) CTG (A-B) = (ctgActgB+1)
/ (ctgB-ctgA)
Double angle formula
Tan2A=2tanA/ (l~tan2A) ctg2A= (ctg2A~l) /2ctga
Cos2a=cos2a-sin2a=2cos2aT=l-2sin2a
Half angle formula
Sin (A/2) = V ((1-cosA) /2) sin (A/2) = V ((1-cosA) /2)
Cos (A/2) = V ((1+cosA) /2) cos (A/2) = V ((1+cosA) /2) Tan (A/2) = V ((1-cosA) / ((1+cosA)) Tan (A/2) = V ((1-cosA) / ((1+cosA))
CTG (A/2) = V ((1+cosA) / ((1-cosA)) CTG (A/2) = V ((1+cosA) / ((1-cosA))