What are the double angle formulas?
Double angle formula:
Sin2A=2SinA。 Kosa
cos2a=cosa^2-sina^2= 1-2sina^2=2cosa^2- 1
tan2A=(2tanA)/( 1-tanA^2)
(Note: Sina 2 is the square of Sina 2 (a))
Double angle formula:
sin2α=2sinαcosα
tan2α=2tanα/( 1-tan^2(α))
cos2α=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)
Triple angle formula:
sin3α=4sinα sin(π/3+α)sin(π/3-α)
cos3α=4cosα cos(π/3+α)cos(π/3-α)
tan3α=tana tan(π/3+a) tan(π/3-a)
What is the 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))
What are the other formulas of trigonometric function?
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]
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)