Mathematical formula in the second volume of the eighth grade:
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? Answer? b |a-b|？ |a|-|b| -|a|？ Answer? |a|
Solution of quadratic equation in one variable-B+? (b2-4ac)/2a -b-？ (b2-4ac)/2a
The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a.
Note: Vieta theorem discriminant b2-4ac=0 Note: The equation has two equal real roots B2-4ac >；; 0
Note: This equation has two unequal real roots B2-4ac.
Note: The equation has no real root, but has a plurality of yokes.
The formula of the sum of two angles of trigonometric function
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-tanA tanB)
tan(A-B)=(tanA-tanB)( 1+tanA tanB)
Sine theorem a/sinA=b/sinB=c/sinC=2R.
Note: where r represents the radius of the circumscribed circle of the triangle.
Cosine theorem b2=a2+c2-2accosB
Note: Angle B is the standard equation (x-a)2+(y-b)2=r2 containing a circle between side A and side C..
Note: (a, b) is the general formula x2+y2+Dx+Ey+F=0.
Note: D2+E2-4f > 0 parabola standard equation y2 = 2pxy2 =-2pxy2 = 2pxy2 =-2pxy
Side area of right-angle prism S=c*h
Side area of oblique prism S=c'*h
The side area of a regular pyramid is S= 1/2c*h'
The side area of the prism is S = 1/2(c+c')h'
The lateral area of the frustum of a cone is s =1/2 (c+c') l = pi (r+r) l.
The surface area of the ball s = 4pi * r.
The lateral area of the cylinder is s = c * h = 2pi * h
The lateral area of the cone is s =1/2 * c * l = pi * r * l.
The arc length formula l=a*r a is the radian number r > of the central angle; 0
Sector formula s= 1/2*l*r
Cone volume formula V= 1/3*S*H
Cone volume formula
Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area and l is the side length.
Cylinder volume formula V=s*h