Sekante
sec α
=
hypotenuse
benachbartes Bein
=
OB
OA
=
OB'
OA'
=
R
xB
Wenn hypotenuse (OB, R, OA') = 1,
sec α = OB'
Funktion
`y = sec x`
Domain
`D(sec x) = R - {-pi/2 + pin, (n in Z)}`
Wertebereich
`E(sec x) = [-infty, -1] uu [1, infty]`
Parität
`eben`
Periodizität
`T = 2pi`
Nullen
`nein`
Konstanzintervalle
`sec x < 0,`
`x in (pi/2+2pin, (3pi)/2+ 2pin), n in Z`
`sec x > 0,`
`x in (-pi/2 + 2pin, pi/2 + 2pin), n in Z`
Intervalle der Monotonie
`uarruarruarr x in [2pin, pi/2 + 2pin)uu`
`uu(pi/2+2pin, pi+2pin], n in Z`
`darrdarrdarr x in [-pi+2pin, -pi/2+2pin)uu`
`uu(-pi/2+2pin, 2pin], n in Z`
Extreme
`y_min = 1, x = 2pin, n in Z`
`y_max = -1, x = pi+2pin, n in Z`
Wendepunkte
`nein`
`sec alpha = 1/cos alpha`
`sec alpha = (tan alpha)/sin alpha`
`sec alpha = text(csc)(alpha+pi/2) = - text(csc)(alpha-pi/2)`
`sec alpha = sec(-alpha)`
`(sec alpha)^' =sin alpha/cos^2 alpha`
`int sec (alpha)dalpha = -ln |tan(pi/2 + alpha/2)| + C`