The principal identities in trigonometry are:
sin^{2}θ + cos^{2}θ = 1
Four trigonometric functions are 2π periodic:
sinθ = sin(θ + 2π)
cosθ = cos(θ + 2π)
cscθ = csc(θ + 2π)
secθ = sec(θ + 2π)
Two trigonometric functions are π periodic:
tanθ = tan(θ + π)
cotθ = cot(θ + π)
Formulas involving sums of angles are as follows:
sin(α + β) = sinαcosβ + cosαsinβ
cos(α + β) = cosαcosβ − sinαsinβ
Substituting β = α gives the double angle formulae
sin(2α) = 2sin(α)cos(α)
cos(2α) = cos^{2}α − sin^{2}α
Substituting sin^{2}α + cos^{2}α = 1 gives
cos(2α) = 2cos^{2}α − 1
cos(2α) = 1 − 2sin^{2}α
sin(3θ) = 3sinθ − 4sin^{3}θ
cos(3θ) = 4cox^{3}θ − 3cosθ
2sin(A)cos(B) = sin(A + B) + sin(A − B)
