sin(A+B) = sinAcosB+cosAsinB
sin(A-B) = sinAcosB-cosAsinB？
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)
cot(A+B)=(cotA cotB- 1)/(cot B+cotA)？
cot(A-B)=(cotA cotB+ 1)/(cot b-cotA)
[Edit this paragraph] Double Angle Formula
Sin2A=2SinA？ Kosa
cos2a=cosa^2-sina^2= 1-2sina^2=2cosa^2- 1
tan2A=2tanA/ 1-tanA^2
[Edit this paragraph] Triple angle formula
tan3a = tan a tan(π/3+a) tan(π/3-a)
[Edit this paragraph] Half-angle formula
[Edit this paragraph] Sum-difference product
sin(a)+sin(b)= 2 sin[(a+b)/2]cos[(a-b)/2]
sin(a)-sin(b)= 2cos[(a+b)/2]sin[(a-b)/2]
cos(a)+cos(b)= 2cos[(a+b)/2]cos[(a-b)/2]
cos(a)-cos(b)=-2 sin[(a+b)/2]sin[(a-b)/2]
tanA+tanB=sin(A+B)/cosAcosB
[Edit this paragraph] Sum and difference of products
sin(a)sin(b)=- 1/2 *[cos(a+b)-cos(a-b)]
cos(a)cos(b)= 1/2 *[cos(a+b)+cos(a-b)]
sin(a)cos(b)= 1/2 *[sin(a+b)+sin(a-b)]
cos(a)sin(b)= 1/2 *[sin(a+b)-sin(a-b)]
[Edit this paragraph] Inductive formula
sin(-a) = -sin(a)
cos(-a) = cos(a)
sin(π/2-a) = cos(a)
cos(π/2-a) = sin(a)
sin(π/2+a) = cos(a)
cos(π/2+a) = -sin(a)
sin(π-a) = sin(a)
cos(π-a) = -cos(a)
sin(π+a) = -sin(a)
cos(π+a) = -cos(a)
tanA= sinA/cosA
tan(π/2+α)=-cotα
tan(π/2-α)=cotα
tan(π-α)=-tanα
tan(π+α)=tanα
[Edit this paragraph] General formula
[Edit this paragraph] Other formulas
[Edit this paragraph] Other non-critical trigonometric functions
csc(a) = 1/sin(a)
Seconds (a)= 1/ cosine (a)
[Edit this paragraph] Hyperbolic function
sinh(a) = [e^a-e^(-a)]/2
cosh(a) = [e^a+e^(-a)]/2
tg h(a) = sin h(a)/cos h(a)
Formula 1:
Let α be an arbitrary angle, and the values of the same trigonometric function with the same angle of the terminal edge are equal:
sin(2kπ+α)= sinα
cos(2kπ+α)= cosα
tan(2kπ+α)= tanα
cot(2kπ+α)= cotα
Equation 2:
Let α be an arbitrary angle, and the relationship between the trigonometric function value of π+α and the trigonometric function value of α;
Sine (π+α) =-Sine α
cos(π+α)= -cosα
tan(π+α)= tanα
cot(π+α)= cotα
Formula 3:
The relationship between arbitrary angle α and the value of-α trigonometric function;
Sine (-α) =-Sine α
cos(-α)= cosα
tan(-α)= -tanα
Kurt (-α) =-Kurt α
Equation 4:
The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:
Sine (π-α) = Sine α
cos(π-α)= -cosα
tan(π-α)= -tanα
cot(π-α)=-coα
Formula 5:
The relationship between the trigonometric function values of 2π-α and α can be obtained by Formula-and Formula 3:
Sine (2π-α)=- Sine α
cos(2π-α)= cosα
tan(2π-α)= -tanα
Kurt (2π-α)=- Kurt α
Equation 6:
The relationship between π/2 α and 3 π/2 α and the trigonometric function value of α;
sin(π/2+α)= cosα
cos(π/2+α)= -sinα
tan(π/2+α)= -cotα
cot(π/2+α)= -tanα
sin(π/2-α)= cosα
cos(π/2-α)= sinα
tan(π/2-α)= cotα
cot(π/2-α)= tanα
sin(3π/2+α)= -cosα
cos(3π/2+α)= sinα
tan(3π/2+α)= -cotα
cot(3π/2+α)= -tanα
sin(3π/2-α)= -cosα
cos(3π/2-α)= -sinα
tan(3π/2-α)= cotα
cot(3π/2-α)= tanα
(higher than k∈Z)
It took me a long time to input this common formula in physics, hoping it will be useful to everyone.
a sin(ωt+θ)+B sin(ωt+φ)= 1
√{(A^2 +B^2 +2ABcos(θ-φ)}？ sin{ ωt + arcsin[ (A？ sinθ+B？ sinφ)/√{a^2 +b^2； +2ABcos(θ-φ)} }
√ indicates the root number, including the contents in {...}.