Summary of common formulas in senior three mathematics
I. Logarithmic function
log.a(MN)=logaM+logN
loga(M/N)=logaM-logaN
logaM^n=nlogaM(n=R)
logbN = logaN/logab(a & gt； 0, b>0, N>0 a and b are not equal to 1)
Second, the area and volume of simple geometry
Rectangular edge of prism =c*h (perimeter of bottom multiplied by height)
S-spine = 1/2*c*h？ (Half of bottom perimeter and slope height)
Let the perimeter of the upper and lower bottom surfaces of the prism be c? , c, and the inclined height is h? ，S= 1/2*(c+c？ )*h
S cylindrical edge =c*l
S frustum edge = 1/2*(c+c? )* l =σ*(r+r？ )*l
S- cone edge =1/2 * c * l = r * r * l.
S ball =4* u * r 3
V cylinder =S*h
V-cone =( 1/3)*S*h
V-ball =(4/3)* Wu * R 3
Third, the positional relationship and distance formula of two straight lines
(1) formula for the distance between two points on the number axis |AB|=|x2-x 1|
(2) The distance formula between two points A (X 1, Y 1) and (X2, Y2) on the plane.
|ab|=sqr[(x2-x 1)^2+(y2-y 1)^2]
(3) The distance formula from point P(x0, y0) to straight line L: Ax+By+C=0 is d=|Ax0+By0+C|/sqr.
(A^2+B^2)
(4) The distance between two parallel straight lines L 1: = AX+BY+C = 0, L2 = AX+BY+C2 = 0 d=|C 1-
C2|/sqr(A^2+B^2)
Basic relations and inductive formulas of trigonometric functions with the same angle
Sin(2*k* Wu +a)=sin(a)
Cos(2*k* u +a)=cosa
Tan(2* u +a)=tana
sin(-a)=-sina，cos(-a)=cosa，tan(-a)=-tana
Sin(2* Uighur -a)=-sina, cos(2* Uighur -a)=cosa, tan(2* Uighur -a)=-tana.
Sin (Wu +a)=- SiNa
Sin(Wu-a)= Sina
Cos (Wu +a)=-cosa
Cos (u -a)=-cosa
Tan (Wu+A) = Tana
Quadruple angle formula and its deformation and application
1, double angle formula
sin2a=2*sina*cosa
cos2a=(cosa)^2-(sina)^2=2*(cosa)^2- 1= 1-2*(sina)^2
tan2a=(2*tana)/[ 1-(tana)^2]
2. The deformation of the double-angle formula
(cosa)^2=( 1+cos2a)/2
(sina)^2=( 1-cos2a)/2
Tan (a/2)= Sina/(1+COSA) = (1-COSA)/Sina.
Five, sine theorem and cosine theorem
Sine theorem:
a/sinA=b/sinB=c/sinC
Cosine theorem:
a^2=b^2+c^2-2bccosA
b^2=a^2+c^2-2accosB
c^2=a^2+b^2-2abcosC
cosA=(b^2+c^2-a^2)/2bc
cosB=(a^2+c^2-b^2)/2ac
cosC=(a^2+b^2-c^2)/2ab
Tan (Wu A) =-Tana
Sin (Wu /2+a)=cosa
Sin (Wu /2-a)=cosa
cos(δ/2+a)=-Sina
Cos (Wu /2-a)= Sina
Tan (Wu /2+a)=-cota
Tan (Wu /2-a)=cota
(sina)^2+(cosa)^2= 1
Sina /cosa=tana
Cosine formula of sum and difference of two angles
cos(a-b)=cosa*cosb+sina*sinb
cos(a-b)=cosa*cosb-sina*sinb
Sine formula of sum and difference of two angles
sin(a+b)=sina*cosb+cosa*sinb
sin(a-b)=sina*cosb-cosa*sinb
Tangent formula of sum and difference of two angles
tan(a+b)=(tana+tanb)/( 1-tana * tanb)