Cosine Theorem B 2 = A 2+C 2-2 ACCOSB 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 x 2+y 2+dx+ey+f = 0 note: d 2+e 2-4f > 0.
Parabolic standard equation y 2 = 2px y 2 =-2px x 2 = 2py x 2 =-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 lateral 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
Cone volume formula V= 1/3*S*H cone 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
Double angle formula
tan2A=2tanA/[ 1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 - 1= 1-2(sina)^2
half-angle formula
sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-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))
cot(A/2)=√(( 1+cosA)/(( 1-cosA))cot(A/2)=-√(( 1+cosA)/(( 1-cosA))？
Sum difference product
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B))
2cosAcosB=cos(A+B)-sin(A-B)
-2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2
cosA+cosB = 2cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB
The sum of the first n terms of some series
1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2
1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= N2
2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1)5
1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+…+n^2=n(n+ 1)(2n+ 1)/6
1^3+2^3+3^3+4^3+5^3+6^3+…n^3=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
Ordinary derivative formula
1.y=c(c is a constant) y'=0
2.y=x^n y'=nx^(n- 1)
3.y=a^x y'=a^xlna
y=e^x y'=e^x
4.y=logax y'=logae/x
y=lnx y'= 1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y = Tanks Y' =1/cos 2x
8.y=cotx y'=- 1/sin^2x
9 . y = arcsinx y'= 1/√ 1-x^2
10 . y = arc cosx y'=- 1/√ 1-x^2
1 1 . y = arctanx y'= 1/ 1+x^2
12 . y = arccotx y'=- 1/ 1+x^2