Matematika Goniometrické funkcie a rovnice - vzorce

cos''x + sin''x = 1
tg x.cotg x = 1
sin (x±y) = sin x.cos y ± cos x.sin y
cos (x+y) = cos x.cos y – sin x.sin y
cos (x-y) = cos x.cos y + sin x.sin y
sin 2x = 2.sin x.cos x
cos 2x = cos''x – sin''x
sin 3x = 3.sin x – 4.sin'''x
cos 3x = 4.cos'''x – 3.cos x
sin x + sin y = 2.sin [(x+y)/2].cos [(x-y)/2]
sin x –sin y = 2.cos [(x+y)/2].sin [(x-y)/2]
cos x + cos y = 2.cos [(x+y)/2].cos [(x-y)/2]
cos x – cos y = -2.sin [(x+y)/2].sin[(x-y)/2]

vysvetlivky:
cos''x = cos na druhú x
cos'''x = cos na tretiu x
cos 2x = cos dva x


sin (90° - α)= cos α
cos (90° - α)= sin α

tg x = sin x/cos x
cotg x = cos x/sin x

V pravouhlom trojuholníku ABC, kde c=prepona; a,b= odvesny; uhol α je oproti strane a, uhol β je oproti strane b, uhol γ je oproti strane c platí:

sin α = a/c
cos α = b/c
tg α = a/b
cotg α = b/a.