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Math Help - [SOLVED] Hyperbolic Function

  1. #1
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    [SOLVED] Hyperbolic Function

    x is a real number and sinh^2(x) = 24/25

    a) what are the possible values of sinh(x)?

    b) what are the possible values of cosh(x)?
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  2. #2
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    Quote Originally Posted by mr_motivator View Post
    x is a real number and sinh^2(x) = 24/25

    a) what are the possible values of sinh(x)?

    Mr F says: Take the square root of both sides of the given equation.

    b) what are the possible values of cosh(x)? Mr F says: Apply the identity {\color{red}\cosh^2 x - \sinh^2 x = 1}.
    What have you tried? Where are you stuck?
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  3. #3
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    Hello, mr_motivator!

    x is a real number and \sinh^2(x) \,=\,\frac{24}{25}

    a) What are the possible values of \sinh(x) ?
    You really don't know how to do this?


    We have: . \sinh^2(x) \:=\:\frac{24}{25}

    . . Then: . \sinh(x) \:=\:\pm\sqrt{\frac{24}{25}} \:=\:\pm\frac{2\sqrt{6}}{5}




    b) What are the possible values of \cosh(x)?

    We're expected to know the identity: . \cosh^2(x) - \sinh^2(x) \:=\:1


    So we have: . \cosh^2(x) \:=\:1 + \sinh^2(x) \:=\:1 + \frac{24}{25} \:=\:\frac{49}{25}

    Therefore: . \cosh(x) \:=\:\sqrt{\frac{49}{25}} \:=\:\frac{7}{5} . .
    (cosh is always positive.)
    .
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