Chapter 5: Everything about Hyperbolic Functions Flashcards
Define the following hyperbolic function:
sinh x
(ex-e-x)/2
Define the following hyperbolic function:
cosh x
(ex+e-x)/2
Define the following hyperbolic function:
tanh x
(sinh x)/(cosh x)
Define the following hyperbolic function:
csch x
1/(sinh x)
Define the following hyperbolic function:
sech x
1/(cosh x)
Define the following hyperbolic function:
coth x
(cosh x)/(sinh x)
Complete the following hyperbolic identity:
sinh(-x) =
-sinh(x)
Complete the following hyperbolic identity:
1 =
(using cosh and sinh)
cosh2(x)-sinh2(x)
Complete the following hyperbolic identity:
cosh(-x) =
cosh(x)
Complete the following hyperbolic identity:
1 - ? = sech2x
? = tanh2(x)
(Can be derived by dividing cosh2x from both sides of identity: cosh2(x)-sinh2(x)=1)
Complete the following hyperbolic identity:
sinh(x+y) =
sinh(x)*cosh(y) + cosh(x)*sinh(y)
Complete the following hyperbolic identity:
cosh(x+y) =
cosh(x)*cosh(y) + sinh(x)*sinh(y)
Find the derivative of the following hyperbolic function:
sinh(x)
cosh(x)
Find the derivative of the following hyperbolic function:
cosh(x)
sinh(x)
Find the derivative of the following hyperbolic function:
tanh(x)
sech2(x)
Find the derivative of the following hyperbolic function:
csch(x)
-csch(x)*coth(x)
Find the derivative of the following hyperbolic function:
sech(x)
-sech(x)*tanh(x)
Find the derivative of the following hyperbolic function:
coth(x)
-csch2(x)
Find the derivative of the following inverse hyperbolic function:
sinh-1(x)
1/sqrt(1+x2)
Find the derivative of the following inverse hyperbolic function:
cosh-1(x)
1/sqrt(x2-1)
Find the derivative of the following inverse hyperbolic function:
tanh-1(x)
1/(1-x2)
Find the derivative of the following inverse hyperbolic function:
csch-1(x)
-1/(|x|sqrt(x2+1))
Find the derivative of the following inverse hyperbolic function:
sech-1(x)
-1/(x*sqrt(1-x2))
Find the derivative of the following inverse hyperbolic function:
coth-1(x)
1/(1-x2)