Tangente
tan α
=
pierna opuesta
pierna adyacente
=
AB
OA
=
A'B'
OA'
=
yB
xB
Si la hipotenusa (OB, OA', R) = 1,
tan α = A'B'
Función
`y = tan x`
Dominio
`D(tan x) = R - {pi/2+pin (n in Z)}`
Rango de valores
`E(tan x) = R`
Paridad
`impar`
Periodicidad
`T = pi`
Ceros
`tan x = 0, x=pin, n in Z`
Intervalos de constancia
`tan x > 0, x in (pin, pi/2 + pin), n in Z`
`tan x < 0, x in (-pi/2 + pin, pin), n in Z`
Intervalos de monotonicidad
`uarruarruarr x in D`
Extremos
`no`
Puntos de inflexión
`y=0, x = pin, n in Z`
`tan alpha = sin alpha / cos alpha`
`tan alpha = 1/text(cot α)`
`tan alpha = - cot(alpha + pi/2) = - cot(alpha - pi/2)`
`tan alpha = sqrt(1/cos^2alpha - 1)`
`-tan alpha = tan(-alpha)`
`(tan alpha)^' =1 /cos^2 alpha`
`int tan(alpha) dalpha = -ln |cos alpha| + C`