Cos,sina,tan,cot

These are the formulas of the triangles.

The triangle is a right angle of two sharp angles in short.

Cos is the cosine theorem, which is the adjacent edge of the acute angle divided by the hypotenuse of the triangle.

Sin is the sine theorem, which is the edge of a sharp angle divided by the hypotenuse of the triangle.

Tan is the tangent theorem, which is the edge of a sharp angle divided by the adjacent edge of a sharp angle.

Cot is the cotangent theorem, which is the adjacent edge of a sharp angle divided by a sharp edge.

Then there is a bunch of conversion formulas, here to do a record, to use the time to look at it ...... ：

Trigonometric Formula
Two corners and formulas
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-TANATANB)
Tan (A-B) = (TANA-TANB)/(1+TANATANB)
Cot (a+b) = (cotAcotB-1)/(Cotb+cota)
Cot (A-B) = (cotacotb+1)/(Cotb-cota)
Double Angle formula
TAN2A = 2tana/(1-tan^2 A)
Sin2a=2sina? CosA
COS2A = cos^2 a--sin^2 A
=2cos^2 A-1
=1-2sin^2 A
Three times-fold angle formula
sin3a = 3sina-4 (SinA) ^3;
cos3a = 4 (CosA) ^3-3cosa
TAN3A = tan A? Tan (π/3+a)? Tan (π/3-a)
Half-width formula
Sin (A/2) =√{(1--cosa)/2}
cos (A/2) =√{(1+cosa)/2}
Tan (A/2) =√{(1--cosa)/(1+cosa)}
Cot (A/2) =√{(1+cosa)/(1-cosa)}
Tan (A/2) = (1--cosa)/sina=sina/(1+cosa)
And the difference of product
Sin (a) +sin (b) = 2sin[(a+b)/2]cos[(a)/2]
Sin (a)-sin (b) = 2cos[(a+b)/2]sin[(a)/2]
Cos (a) +cos (b) = 2cos[(a+b)/2]cos[(a)/2]
Cos (a)-cos (b) = -2sin[(a+b)/2]sin[(a)/2]
Tana+tanb=sin (a+b)/COSACOSB
The accumulation and difference of
Sin (a) sin (b) = -1/2*[cos (a+b)-cos (a)]
cos (a) cos (b) = 1/2*[cos (a+b) +cos (a)]
Sin (a) cos (b) = 1/2*[sin (a+b) +sin (a)]
cos (a) sin (b) = 1/2*[sin (a+b)-sin (a)]
Induction 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)
Tga=tana = Sina/cosa
Universal formula
Sin (a) = [2tan (A/2)]/{1+[tan (A/2)]^2}
cos (a) = {1-[tan (A/2)]^2}/{1+[tan (A/2)]^2}
Tan (a) = [2tan (A/2)]/{1-[tan (A/2)]^2}
Other formulas
Sin (a) +b?cos (a) = [√ (a^2+b^2)]*sin (a+c) [Where, Tan (c) =b/a]
Sin (a)-b?cos (a) = [√ (a^2+b^2)]*cos (a-c) [Where, Tan (c) =a/b]
1+sin (a) = [sin (A/2) +cos (A/2)]^2;
1-sin (a) = [sin (A/2)-cos (A/2)]^2;
Other non-focused trigonometric functions

SEC (A) = 1/cos (a)
Hyperbolic functions
Sinh (a) = [e^a-e^ (-a)]/2
Cosh (a) = [e^a+e^ (-a)]/2
TG h (a) = sin h (a)/cos H (a)
Formula One:
Set α to an arbitrary angle, with the same trigonometric function values equal to the same angle of the end edge:
Sin (2kπ+α) = sine
cos (2kπ+α) = Cosα
Tan (2kπ+α) = Tanα
Cot (2kπ+α) = Cotα
Formula Two:
The relationship between the trigonometric function value of π+α and the trigonometric function value of α is set to α as an arbitrary angle:
Sin (π+α) =-sinα
cos (π+α) =-cosα
Tan (π+α) = Tanα
Cot (π+α) = Cotα
Formula Three:
Relationship between the trigonometric function values of arbitrary angular α and-α:
Sin (-α) =-sinα
cos (-α) = Cosα
Tan (-α) =-tanα
Cot (-α) =-cotα
Formula Four:
The relationship between the trigonometric function values of π-α and α can be obtained by using Formula Two and Formula Three:
Sin (π-α) = sine
cos (π-α) =-cosα
Tan (π-α) =-tanα
Cot (π-α) =-cotα
Formula Five:
The relationship between the trigonometric function values of 2π-α and α can be obtained by using formula-and Formula Three:
Sin (2π-α) =-sinα
cos (2π-α) = Cosα
Tan (2π-α) =-tanα
Cot (2π-α) =-cotα
Formula Six:
The relationship between Π/2±α and the trigonometric function values of 3π/2±α and α:
Sin (π/2+α) = Cosα
cos (π/2+α) =-sinα

Cos,sina,tan,cot