1. ## [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)?

2. Originally Posted by mr_motivator
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?

3. 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.)
.