Reciprocal relation: tan α cotα =1sin α CSC α =1cos α secα =1quotient relation: sin α/cos α = tan α = secα/CSC α cos α/sin α = cotα = CSC α/secα square relation: sin2 (α).

Two commonly used formulas under different conditions

Sin? α+cos？ α= 1 tan α *cot α= 1

Special formula

(Sina+sinθ) * (Sina+sinθ) = sin (a+θ) * sin (a-θ) Proof: (Sina+sinθ) * (Sina+sinθ) = 2sin [(θ+a)/2] cos [(a-θ)/2].

Acute angle formula of trigonometric function

Sine: the hypotenuse cosine of the opposite side of sin α = ∠ α/α: the hypotenuse tangent of the adjacent side of cos α = ∠ α/α: the cotangent of the opposite side of tan α = ∠ α/α = ∠α.

Double angle formula

Sin2A=2sinA cosA Cosa cosine 1. cos2a = cos 2(a)-sin 2(a)= 2cos 2(a)- 1 = 1-2 sin 2(a)2。 Cos2a = 65438。

half-angle formula

tan(A/2)=( 1-cosA)/sinA = sinA/( 1+cosA)； cot(A/2)= sinA/( 1-cosA)=( 1+cosA)/sinA。 sin^2(a/2)=( 1-cos(a))/2 cos^2(a/2)=( 1+cos(a))/2 tan(a/2)=( 1-cos(a))/sin(a)= sin(a)/( 1+cos(a))

Sum difference product

sinθ+sinφ= 2 sin[(θ+φ)/2]cos[(θ-φ)/2]

sinθ-sinφ= 2 cos[(θ+φ)/2]sin[(θ-φ)/2]cosθ+cosφ= 2 cos[(θ+φ)/2]cosθ-cosφ=-2 sin[(θ+φ)/2]sin[(θ+φ)/2]tanA+tanB = sin(A+B)/cosa cosb = tan(A+B)( 1-tanA tanB)tanA-tanB = sin(A-B)/cosa cosb = tan(

Two-angle sum formula

cos(α+β)= cosαcosβ-sinαsinβcos(α-β)= cosαcosβ+sinαsinβsin(α+β)= sinαcosβ+cosαsinβsin(α-β)= sinαcosβ-cosαsinβ

Sum and difference of products

sinαsinβ=[cos(α-β)-cos(α+β)]/2 cosαcosβ=[cos(α+β)+cos(α-β)]/2 sinαcosβ=[sin(α+β)+sin(α-β)]/2 cosαsinβ=[sin(α+β)-sin(α-β)]

Inductive formula

sin(-α)=-sinαcos(-α)= cosαtan(-α)=-tanαsin(π/2-α)= cosαcos(π/2-α)= sinαsin(π/2+α)= cosαcos(π/2+α)=-sinαsin(π-α)= sinαcos(π-α)=-cosαsin(π+α) =-sinαcos(π+α)=-sinαcos(π+α)=-cosαtana = Sina/Cosatan(π/2+α)=-sin

General formula of trigonometric function

sinα= 2tan(α/2)/[ 1+(tan(α/2))？ ] cosα=[ 1-(tan(α/2))？ ]/[ 1+(tan(α/2))？ ]tanα= 2tan(α/2)/[ 1-(tan(α/2))？ ]