Calculus

If tanh(x)=24/25, find the values of the other hyperbolic function at x

I was able to find coth(x)=25/24, but what is sin, cos, csc, and sec?

I would greatly appreciate your help!!

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  1. use the definition of tanh(x)

    tanh(x) = (e^2x -1)/(e^2x + 1)

    (e^2x -1)/(e^2x + 1) = 24/25
    25e^2x - 25 = 24e^2x + 24
    e^2x = 49
    take √
    e^x = ±7

    then
    sinh(x) = (1/2)(e^x - e^-x)
    = (1/2)(7 - 1/7)
    = (1/2)(48/7) = 24/7

    cosh(x) = (1/2)(e^x + e^-x)
    = (1/2)(7 + 1/7) = 24/7

    You will find the definitions of the hyperbolic trig functions here

    http://en.wikipedia.org/wiki/Hyperbolic_function#Standard_algebraic_expressions

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  2. Actually- cosh(x) = (1/2)(e^x + e^-x)
    = (1/2)(7 + 1/7) = 25/7, not 24/7

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