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)
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
Rectangular common graphic area formula = length× width S = ab
Area of a square = side length × side length S = a?
Area of triangle = base × height ÷2 S=ah÷2.
Area of parallelogram = base × height S=ah
Trapezoidal area = (upper bottom+lower bottom) × height ÷2 S=(a+b)h÷2.
Area of circle = π× radius× radius
Factorization formula square difference formula: a? -B? =(a+b)(a-b).
Complete square formula: a? +2ab+b？ =(a+b)？ .
Cubic sum formula: a? +b？ =(a+b)(a？ -ab+b？ )。
Cubic difference formula: a? -B? =(a-b)(a？ +ab+b？ )。
Complete cubic sum formula: a? +3a？ b+3ab？ +b？ =(a+b)？ .
Complete cubic difference formula: a? -3a？ b+3ab？ -B? =(a-b)？ .
Three complete square formulas: a? +b？ +c？ +2ab+2bc+2ac=(a+b+c)？ .
Formula of cubic sum of three terms: a? +b？ +c？ -3abc=(a+b+c)(a？ +b？ +c？ -ab-bc-ac).
Volume formula of the ball Volume formula of the ball: the volume of the ball with radius r.
The formula is: v = (4/3) π r 3 (three quarters times π times the radius of the cube).
V = (1/6) π d 3 (one sixth times π times the third power of diameter)