[SOLVED] Hyperbolic Function

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February 5th 2009, 04:24 PM
mr_motivator

[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)?
February 5th 2009, 04:56 PM
mr fantastic

Quote:

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?
February 5th 2009, 05:00 PM
Soroban

Hello, mr_motivator!

Quote:

$x$ 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: . $\sinh(x) \:=\:\pm\sqrt{\frac{24}{25}} \:=\:\pm\frac{2\sqrt{6}}{5}$

Quote:

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.)
.

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