# If cosh(x)=25/24 and x>0, how do you find the values of the other hyperbolic functions at x?

Jul 26, 2016

Given $\cosh x = \frac{25}{24} , \sinh x = \pm \frac{7}{24} \mathmr{and} \tanh x = \pm \frac{7}{25}$ The other three funtctions sech x, csch x and coth x are reciprocals.

#### Explanation:

Use ${\cosh}^{2} x - {\sinh}^{2} x = 1 \mathmr{and} \tanh x = \sinh \frac{x}{\cosh} x$.

Here, $\cosh x = \frac{25}{24}$.

So, $\sinh x = \pm \sqrt{{\cosh}^{2} x - 1} = \pm \sqrt{{\left(\frac{25}{24}\right)}^{2} - 1} = \pm \frac{7}{24}$ and

$\tanh x = \sinh \frac{x}{\cosh} x = \pm \frac{7}{25}$.

Negative sign is chosen, when x < 0.

y = cosh x is an even function of

of x, and so, inversely, it is $1 \to 2$ mapping, giving $\pm x$ against y