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)?
Hello, mr_motivator!
You really don't know how to do this?$\displaystyle x$ is a real number and $\displaystyle \sinh^2(x) \,=\,\frac{24}{25}$
a) What are the possible values of $\displaystyle \sinh(x)$ ?
We have: .$\displaystyle \sinh^2(x) \:=\:\frac{24}{25}$
. . Then: .$\displaystyle \sinh(x) \:=\:\pm\sqrt{\frac{24}{25}} \:=\:\pm\frac{2\sqrt{6}}{5}$
b) What are the possible values of $\displaystyle \cosh(x)$?
We're expected to know the identity: .$\displaystyle \cosh^2(x) - \sinh^2(x) \:=\:1$
So we have: .$\displaystyle \cosh^2(x) \:=\:1 + \sinh^2(x) \:=\:1 + \frac{24}{25} \:=\:\frac{49}{25}$
Therefore: .$\displaystyle \cosh(x) \:=\:\sqrt{\frac{49}{25}} \:=\:\frac{7}{5}$ . . (cosh is always positive.)
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