5.7 Hyperbolic Functions
Def: The hyperbolic functions we the following
sinhla) = exe" costarse atter tube); sights
2
2
=
Cash(x)
1
<school=
Sinhas) sech(x) = shack) coth(x) = Funkcio
Funk(x)
jzer
y=sin(8)
=
sinh
e
Curves of the form
Ca Cosh!)
Ja
are
Lim
470
C
I'm ex
K8-0 été
=
x+
x
مرار
te
-Y
-2K
=
x+x
-
e&
1
itA. of y = ± 4
called catening curves
米
,5.7 Cont.
HyonColic Identities
•2 (chi) = costal (even)
tush(x) rinkta (
1. 1-tank²(a) = seckin
5. Hinh (x+y)=sinhas coshly) +ossly) sindices
6. Cosh (ty)= (shalcalcy) + sinh(s) sinlay)
Proof I
inli(-x): e
Bost of 3.
2
-
2
-achter - Finktus = (c²+ ")² - (every z
sin(x)
2
2
2
It.
2/4) = 1
If cashows = && and xx, nd the values of the other
hyper dic functions of x
[5] = sub_/
16 = sint² (x) x70 inches zo
=
-sintex)=1
4
15 hos
Sinhala & cortices = {
table & 446)==
~SC, h(x) = 1
sesbaw) = 5 cothaels
fi fi
Def: The hyperbolic functions we the following
sinhla) = exe" costarse atter tube); sights
2
2
=
Cash(x)
1
<school=
Sinhas) sech(x) = shack) coth(x) = Funkcio
Funk(x)
jzer
y=sin(8)
=
sinh
e
Curves of the form
Ca Cosh!)
Ja
are
Lim
470
C
I'm ex
K8-0 été
=
x+
x
مرار
te
-Y
-2K
=
x+x
-
e&
1
itA. of y = ± 4
called catening curves
米
,5.7 Cont.
HyonColic Identities
•2 (chi) = costal (even)
tush(x) rinkta (
1. 1-tank²(a) = seckin
5. Hinh (x+y)=sinhas coshly) +ossly) sindices
6. Cosh (ty)= (shalcalcy) + sinh(s) sinlay)
Proof I
inli(-x): e
Bost of 3.
2
-
2
-achter - Finktus = (c²+ ")² - (every z
sin(x)
2
2
2
It.
2/4) = 1
If cashows = && and xx, nd the values of the other
hyper dic functions of x
[5] = sub_/
16 = sint² (x) x70 inches zo
=
-sintex)=1
4
15 hos
Sinhala & cortices = {
table & 446)==
~SC, h(x) = 1
sesbaw) = 5 cothaels
fi fi
