The relationship between root and coefficient x1x2 =-b/ax1* x2 = c/a Note: Vieta theorem.
Discriminant b2-4a=0 Note: The equation has two equal real roots.
B2-4ac >0 Note: The equation has real roots.
B2-4ac & lt； 0 Note: The equation has multiple yokes.
formulas of trigonometric functions
Two-angle summation formula sin (a b) = sinacosb cosa sinbsin (a b) = sinacosb-sinbcosa.
cos(A B)=cosAcosB-sinAsinB
tan(A B)=(tanA tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1 tanA tanB)
ctg(A B)=(ctgActgB- 1)/(ctgB ctgA)ctg(A-B)=(ctgActgB 1)/(ctgB-ctgA)
The angle doubling 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 2sina cosb = sin (ab) sin (a-b) 2cosasinb = sin (ab)-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)/sinAsinB
The sum of the first n items in some sequences is123456789 … n = n (n1)/21357911315 … (2n-/kloc-.
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 * 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: Angle B is the included angle between side A and side C..
The standard equation of a circle (x-a)2 (y-b)2=r2 Note: (A, B) is the center coordinate.
General equation of circle x2 y2 Dx Ey F=0 Note: d2e 2-4f >；; 0
Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py
Lateral area of a straight prism S=c*h lateral area of an oblique prism s = c' * h.
Lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c c')h'
The side surface area of the frustum of a cone S = 1/2(c c')l = pi(R R)l The surface area of the ball S=4pi*r2.
Lateral area of cylinder S=c*h=2pi*h lateral area of cone 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 area formula s= 1/2*l*r
Conical volume formula V= 1/3*S*H Conical volume formula V= 1/3*pi*r2h
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 cylinder V=pi*r2h