Opposite side/hypotenuse of sinα=∞α
Adjacent edge/hypotenuse of cosα=∞α
Opposite side of tanα = adjacent side of ∠ α/∠α.
Adjacent side of cotα = opposite side of ∠ α/∠α.
Double angle formula
Sin2A=2SinA? Kosa
Cos2A=CosA? -Sina? = 1-2SinA? =2CosA? - 1
tan2A=(2tanA)/( 1-tanA? )
(Note: Sina? Is the square of Sina, sin2(A))
Triple angle formula
sin3α=4sinα sin(π/3+α)sin(π/3-α)
cos3α=4cosα cos(π/3+α)cos(π/3-α)
tan3a=tana tan(π/3+a) tan(π/3-a)
Derivation of triple angle formula
sin3a = sin(2a+a)= sin 2 acosa+cos 2 asina
Auxiliary angle formula of trigonometric function
Asinα+Bcosα=(A? +B? )' (1/2)sin(α+t), where
sint=B/(A? +B? )'( 1/2)
Cost =A/(A? +B? )'( 1/2)
tant=B/A
Asinα+Bcosα=(A? +B? )'( 1/2)cos(α-t),tant=A/B
Reduced power formula
Sin? (α)=( 1-cos(2α))/2 = versin(2α)/2
Because? (α)=( 1+cos(2α))/2 = covers(2α)/2
Tan? (α)=( 1-cos(2α))/( 1+cos(2α))