# If sinh x = 3/2, how do you find exact values for cosh x and tanh x?

Aug 25, 2016

$\cosh x = \frac{\sqrt{13}}{2}$.

$\tanh x = \frac{3}{\sqrt{13}}$.

#### Explanation:

WE know that, ${\cosh}^{2} x - {\sinh}^{2} x = 1$.

Hence, ${\cosh}^{2} x = {\sinh}^{2} x + 1 = {\left(\frac{3}{2}\right)}^{2} + 1 = \frac{13}{4}$

$\therefore \cosh x = \frac{\sqrt{13}}{2}$.

$\tanh x = \sinh \frac{x}{\cosh} x = \frac{3}{\sqrt{13}}$.