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Calculate sinh x given cosh x = 5/4 and x > 0

Find the value of \sinh x given that \cosh x = \frac{5}{4} and x > 0.


We know \sinh^2 x = \cosh^2 x - 1. So, if \cosh x = \frac{5}{4} we have

    \[ \sinh^2 x = \frac{25}{16} - 1 = \frac{9}{16}. \]

Thus, if x > 0,

    \[ \sinh x = \frac{3}{4}. \]

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