Below is a value of cosh. Use the definitions for hyperbolic functions and the i

Question

Below is a value of cosh. Use the definitions for hyperbolic functions and the identity cosh 2x-sinh 2x-1 to find the values of the remaining fve hyperbolc tnctions 25 cosh x = x > 0 What is the value of sinh x? sinh x= | | (Type an integer or a simplified fraction.) What is the value of tanh x? tanh x = (Type an integer or a simplified fraction.) What is the value of coth x? oxType an integer or a simplified fraction.) What is the value of sech x? secx(Type an integer or a simplified fraction.) What is the value of csch x? cschx Type an integer or a simplified fraction.)

Explanation / Answer

cosh²(x) -sinh²(x)=1

cosh²(x) = 1 + sinh²(x)
x > 0 means that sinh(x) > 0

cosh(x) = 25/7
cosh²(x) = 625/49

sinh²(x) =cosh²(x) - 1
sinh²(x) = 625/49 - 1 = 576/49
sinh(x) = 24/7

tanh(x) = sinh(x)/cosh(x)

= ( 24/7 )/(25/7)

tanh(x)=24/25

coth(x) = 1/tanh(x) = 25/24

csch(x) = 1/sinh(x) = 7/24

sechx=1/cosh(x)=7/25

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