Formelsammlung zur Trigonometrie Definition

sin! =Gegenkathete!von!!

Hypotenuse cos! =

Ankathete!von!!

Hypotenuse tan! =

Gegenkathete!von!!

Ankathete!von!!

Merkdreieck

sin !

cos !

1

!

90°-!

Zusammenhänge sin! = cos(90° "! ) cos! = sin(90° "! ) sin2! + cos

2! = 1

tan! =sin!

cos!

Graphen

sin α cos α Besondere Werte

α 0° 30° 45° 60° 90° sin α 1

2! 0 = 0 1

2! 1 =

1

2 1

2! 2 1

2! 3 1

2! 4 = 1

cos α 1

2! 4 = 1 1

2! 3 1

2! 2 1

2! 1 =

1

2 1

2! 0 = 0

Negative Winkel sin(!" ) =!! sin" cos(!" ) =!cos" Additionstheoreme sin(! ± ") = sin! # cos" ± cos! # sin"

cos(! ± ") = cos! # cos" ! sin! # sin"

Formeln für doppelte Winkel (Additionstheoreme für α = β) sin(2! ) = 2 " sin! " cos! cos(2! ) = cos2! " sin

2! = 2 # cos

2! "1