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Math Help - problem with finding values

  1. #1
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    problem with finding values

    Hi
    I have problem with the following:
    Find the value of one of the six hyperbolic functions for x:
    cosh(x)=\frac{5}{4}

    P.S
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  2. #2
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    Hello, Paymemoney!

    I don't understand the question . . .


    Find the value of one of the six hyperbolic functions for x:

    . . \cosh(x)=\frac{5}{4}\qquad{\color{blue}\Leftarrow\  ;\;\text{We have one!}}

    So what's the problem?
    If they mean find another one . . .


    \text{Since }\,\cosh^2\!x - \sin^2\!x \:=\:1,\,\text{ then: }\:\sinh x \;=\;\pm\sqrt{\cosh^2\!h - 1}

    \text{Hence: }\:\sinh x \;=\;\pm\sqrt{\left(\frac{5}{4}\right)^2-1} \;=\;\pm\sqrt{\frac{9}{16}}

    Therefore: . \sinh x \;=\;\pm\frac{3}{4}


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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, Paymemoney!

    I don't understand the question . . .


    If they mean find another one . . .


    \text{Since }\,\cosh^2\!x - \sin^2\!x \:=\:1,\,\text{ then: }\:\sinh x \;=\;\pm\sqrt{\cosh^2\!h - 1}

    \text{Hence: }\:\sinh x \;=\;\pm\sqrt{\left(\frac{5}{4}\right)^2-1} \;=\;\pm\sqrt{\frac{9}{16}}

    Therefore: . \sinh x \;=\;\pm\frac{3}{4}


    yeh this is what i mean
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