formulas of trigonometric functions

Two-angle sum formula

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)

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)=√(( 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))

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)

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

tanA-tanB=sin(A-B)/cosAcosB

ctgA+ctgBsin(A+B)/sinAsinB

-ctgA+ctgBsin(A+B)/sinAsinB

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)

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 law

a/sinA=b/sinB=c/sinC=2R

note:

In ...

rare

Represents the radius of the circumscribed circle of a triangle.

cosine theorem

B2 = a2+C2-2 acco b

Note: Angle B is the included angle between side A and side C..

the standard equation of the circle

(x-a)2+(y-b)2=r2

Note: (a, b) is the central coordinate.

Circular general equation

x2+y2+Dx+Ey+F=0

Note: D2+E2-4f > 0

Parabolic standard equation

y2=2px

y2=-2px

x2=2py

x2=-2py

Transverse area of right prism

S=c*h

Oblique prism side area

S=c'*h

Side area of regular pyramid

S= 1/2c*h '

Transverse area of regular prism

S= 1/2(c+c')h '

Yuantai lateral area

s = 1/2(c+c’)l = pi(R+R)l

Surface area of ball

S=4pi*r2

Cylindrical side area

S=c*h=2pi*h

Cone lateral area

S= 1/2*c*l=pi*r*l

Arc length formula

l=a*r

A is the radian number r of the central angle

& gt0

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 area of the straight line,

L is the length of the side.

Cylinder volume formula

V=s*h

cylinder

V=pi*r2h

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=tanx

y'= 1/cos^2x

8.y=cotx

y'=- 1/sin^2x

9.y=arcsinx

y'= 1/√ 1-x^2

10.y=arccosx

y'=- 1/√ 1-x^2

1 1.y=arctanx

y'= 1/ 1+x^2

12.y=arccotx

y'=- 1/ 1+x^2