If cosh(x)=25/24 and x>0, how do you find the values of the other hyperbolic functions at x?

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Answer 1 · 2016-07-26T12:07:22

Given #cosh x = 25/24, sinh x = +-7/24 and tanh x = +-7/25# The other three funtctions sech x, csch x and coth x are reciprocals.

Use #cosh^2x-sinh^2x=1 and tanh x = sinh x/cosh x#.

Here, #cosh x = 25/24#.

So, #sinh x = +-sqrt(cosh^2x-1)=+-sqrt((25/24)^2-1)=+-7/24# and

#tanh x = sinh x/cosh x=+-7/25#.

Negative sign is chosen, when x < 0.

y = cosh x is an even function of

of x, and so, inversely, it is #1 to 2 # mapping, giving #+-x# against y