Square relation:
sin^2(α)+cos^2(α)= 1
tan^2(α)+ 1=sec^2(α)
cot^2(α)+ 1=csc^2(α)
Relationship between products:
sinα=tanα*cosα cosα=cotα*sinα
tanα=sinα*secα cotα=cosα*cscα
secα= tanα* CSCαcsα= secα* cotα
Reciprocal relationship:
tanα cotα= 1
sinα cscα= 1
cosα secα= 1
Constant deformation formula of trigonometric function
Trigonometric function of sum and difference of two angles;
cos(α+β)=cosα cosβ-sinα sinβ
cos(α-β)=cosα cosβ+sinα sinβ
sin(α β)=sinα cosβ cosα sinβ
tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)
tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)
Auxiliary angle formula:
Asinα+bcosα = (A2+B2) (1/2) sin (α+t), where
sint=B/(A^2+B^2)^( 1/2)
cost=A/(A^2+B^2)^( 1/2)
Double angle formula:
sin(2α)=2sinα cosα=2/(tanα+cotα)
cos(2α)=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)
tan(2α)=2tanα/[ 1-tan^2(α)]
Triple angle formula:
sin3α=3sinα-4sin^3(α)
cos3α=4cos^3(α)-3cosα
Half-angle formula:
Sin(α/2)= plus or minus √(( 1-cosα)/2)
Cos(α/2)= plus or minus √(( 1+cosα)/2)
Tan(α/2)= plus or minus √ ((kloc-0/-cosα)/(kloc-0/+cosα)) = sinα/(1+cosα) = (1-cosα)/sinα.
Power reduction formula
sin^2(α)=( 1-cos(2α))/2
cos^2(α)=( 1+cos(2α))/2
tan^2(α)=( 1-cos(2α))/( 1+cos(2α))
General formula:
sinα=2tan(α/2)/[ 1+tan^2(α/2)]
cosα=[ 1-tan^2(α/2)]/[ 1+tan^2(α/2)]
tanα=2tan(α/2)/[ 1-tan^2(α/2)]
Product sum and difference formula:
sinαcosβ=( 1/2)[sin(α+β)+sin(α-β)]
cosαsinβ=( 1/2)[sin(α+β)-sin(α-β)]
cosαcosβ=( 1/2)[cos(α+β)+cos(α-β)]
sinαsinβ=-( 1/2)[cos(α+β)-cos(α-β)]
Sum-difference product formula:
sinα+sinβ= 2 sin[(α+β)/2]cos[(α-β)/2]
sinα-sinβ= 2cos[(α+β)/2]sin[(α-β)/2]
cosα+cosβ= 2cos[(α+β)/2]cos[(α-β)/2]
cosα-cosβ=-2 sin[(α+β)/2]sin[(α-β)/2]
* Others:
sinα+sin(α+2π/n)+sin(α+2π* 2/n)+sin(α+2π* 3/n)+……+sin[α+2π*(n- 1)/n]= 0
Cos α+cos (α+2π/n)+cos (α+2π * 2/n)+cos (α+2π * 3/n)+...+cos [α+2π * (n-1)/n] = 0 and
sin^2(α)+sin^2(α-2π/3)+sin^2(α+2π/3)=3/2
tanAtanBtan(A+B)+tanA+tan B- tan(A+B)= 0