Mathematical formula meaning:
It is an expression that people find some connection between things in nature and express it in some way. It is the equal or unequal relationship between the quantities of different things in nature, accurately reflects the internal and external relations of things, and is the basis for us to reach another thing from one thing, so as to better understand the essence and connotation of things.
Common mathematical formulas:
Multiplication and factorization A2-B2 = (a+b) (a-b) A3+B3 = (a+b) (A2-AB+B2) A3-B3 = (a-b) (A2+AB+B2)?
Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B || A |≤ B < = > -b≤a≤b？ |a-b|≥|a|-|b| -|a|≤a≤|a|
Solution of quadratic equation in one variable -b+√(b2-4ac)/2a? -b-b+√(b2-4ac)/2a
The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a note: Vieta theorem?
Discriminant b2-4a=0? Note: Does the equation have two equal real roots?
b2-4ac >0 ? Note: Does the equation have a real root?
B2-4ac & lt； 0 ? Note: How many yokes does the equation have?
formulas of trigonometric functions
Two-angle summation formula sin (a+b) = sinacosb+cosasinbsin (a-b) = sinacosb-sinbcosa?
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb？
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)？
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)？
Double angle formula tan2a = 2tana/(1-tan2a) ctg2a = (ctg2a-1)/2ctga?
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a？
Half-angle formula sin (a/2) = √ ((kloc-0/-COSA)/2) sin (a/2) =-√ ((kloc-0/-COSA)/2)?
cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)？
tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))？
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))？
Sum-difference product 2sinacosb = sin (a+b)+sin (a-b) 2cosasinb = sin (a+b)-sin (a-b)?
2 cosa cosb = cos(A+B)-sin(A-B)-2 Sina sinb = cos(A+B)-cos(A-B)？
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)？
tanA+tanB = sin(A+B)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb？
ctgA+ctgBsin(A+B)/Sina sin B-ctgA+ctgBsin(A+B)/Sina sinb？
The sum of the first n terms in some sequences is1+2+3+4+5+6+7+8+9+…+n = n (n+1)/21+3+5+7+9+/kloc-0.
2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6？
13+23+33+43+53+63+…n3 = N2(n+ 1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3？
Sine theorem? A/sinA=b/sinB=c/sinC=2R Note: Where r represents the radius of the circumscribed circle of a triangle?
Cosine theorem? B2=a2+c2-2accosB Note: Is angle B the included angle between side A and side C?
Standard equation of a circle? (x-a)2+(y-b)2=r2 Note: (a, b) is the central coordinate?
General equation of a circle? X2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0 ?
Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py?
Straight prism lateral area? S=c*h side area of oblique prism S=c'*h
Lateral area, a right pyramid? S= 1/2c*h' prism side area? S= 1/2(c+c')h '
Horizontal area? S = 1/2(c+c')l = pi(R+R)l What is the surface area of the ball? S=4pi*r2