7/23/2019 FUNCIONES HIPERBLICAS 5

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FUNCIONES HIPERBLICAS

Senh x =2

xx

ee

cosh x =

2

xx

ee

+ tgh x =

xx

xx

ee

ee

+

DERIVADAS INTEGRALES

dx

d (senh u) = u. cosh u senh u . du = cosh u + c

dx

d (cosh u) = u. senh u cosh u . du = senh u + c

dx

d (tgh u) = u . sech2 u sech2 u . du = tgh u + c

dx

d

(ctgh u) = - u . csch2u csch2u . du = ctgh u + c

dx

d (sech u) = - u . sech u tgh u sech u . tgh u . du = - sech u +

c

dx

d (csch u) = - u . csch u ctgh u csch u . ctgh u . du = -csch u +

c

tgh u . du = Ln cosh u+ c

VALORES DE LAS FUNCIONES TRIGONOMTRICAS

0 , 360 30 45 60 90 120 150 180 20

0, 2 ! 6 ! 4 ! 3 ! 2 2! 3 5! 6 3! 2sen 0 1 ! 2 2!2 2!3 1 2!3 1 ! 2 0 - 1

cos 1 2!3 2!2 1 ! 2 0 - 1 ! 2 - 2!3 - 1 0

tg 0 3!3 1 3 - 3 - 3!3 0 cot 3 1 3!3 0 - 3!3 - 3 0sec 1 2

3!3

2 2 - 2 - 2 3!3 - 1

csc 2 2 23!3

1 2

3!3

2 - 1

" Z " = " + (- 1)" #$%$ seno & cosec$nteSo'ucn de

= *ngu'o #%nc$' " = 2" #$%$ coseno & sec$nte un$ cu$cn %gono/t%c$

"= So'ucn ene%$' " = " #$%$ t$ngente & cot$ngente