If tanh(x) = 5/13 , find the values of the other hyperbolic functions at x.

Solution:

Given, tanh(x) = 5/13

We have to find the values of the other hyperbolic functions at x.

tanx = sinx/cosx

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

perpendicular = 5, base = 12 and hypotenuse = 13

cosh(x) = b/h = 12/13 and sinh(x) = p/h = 5/13

We know, cosecx = 1/sinx

So, cosech(x) = 1/sinh(x)

cosech(x) = 13/5

We know, secx = 1/cosx

So, sech(x) = 1/cosh(x)

sech(x) = 13/12

We know, cotx = 1/tanx

So, coth(x) = 1/tanh(x)

coth(x) = 1/(5/13)

coth(x) = 13/5

Therefore, the values of other hyperbolic functions at x are sinh(x) = 5/13, cosh(x) = 12/13, cosech(x) = 13/5, sech(x) = 13/12 and coth(x) = 13/5.

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If tanh(x) = 5/13 , find the values of the other hyperbolic functions at x.

Summary:

If tanh(x) = 5/13 , the values of the other hyperbolic functions at x are sinh(x) = 5/13, cosh(x) = 12/13, cosech(x) = 13/5, sech(x) = 13/12 and coth(x) = 13/5.