Sinus
sin α
=
gegenüberliegendes Bein
hypotenuse
=
AB
OB
=
yB
R
Wenn hypotenuse (OB, R) = 1,
sin α = gegenüberliegendes Bein (AB, yB)
Funktion
`y = sin x`
Domain
`D(sin x) = R`
Wertebereich
`E(sin x) = [-1, 1]`
Parität
`seltsam`
Periodizität
`T = 2pi`
Nullen
`sin x = 0, x=pin, n in Z`
Konstanzintervalle
`sin x < 0, x in (2pin, pi + 2pin), n in Z`
`sin x > 0, x in (-pi + 2pin, 2pin), n in Z`
Intervalle der Monotonie
`uarruarruarr x in [-pi/2 + 2pin, pi/2 + 2pin], n in Z`
`darrdarrdarr x in [pi/2 + 2pin, (3pi)/2 + 2pin], n in Z`
Extreme
`y_min = -1, x = -pi/2+2pin, n in Z`
`y_max = 1, x = pi/2+2pin, n in Z`
Wendepunkte
`y=0, x = pin, n in Z`
`sin alpha = cos(alpha - pi/2)`
`sin alpha = +- sqrt(1 - cos^2alpha)`
`sin alpha = cos alpha * text(tan α)`
`sin alpha = cos alpha / text(cot α)`
`sin alpha = - sin(-alpha)`
`(sin alpha)^' =cos alpha`
`int sin (alpha)dalpha = -cos alpha + C`
`alpha*cos alpha < sin alpha < alpha, 0< alpha< 1`