Mathematics: If cosh x = 13 5 and x 0, find the values of the other hyperbolic functions at x.

If cosh x = 13 5 and x 0, find the values of the

Ответ:

xcapo1x

04.01.2022

Recall that

$\cosh^2x-\sinh^2x=1\implies \cosh x=\pm\sqrt{1+\sinh^2x}$

You're given that $\cosh x=\dfrac{13}50$ , so omit the negative root. Then

$\dfrac{13}5=\sqrt{1+\sinh^2x}\implies\sinh^2x=\dfrac{144}{25}\implies\sinh x=\pm\dfrac{12}5$

Because

, you have $\sinh x0$ too, so omit the negative root again. Then $\sinh x=\dfrac{12}5$ .

Now,

$\mbox{sech }x=\dfrac1{\cosh x}=\dfrac5{13}$
$\mbox{csch }x=\dfrac1{\sinh x}=\dfrac5{12}$
$\tanh x=\dfrac{\sinh x}{\cosh x}=\dfrac{\frac{12}5}{\frac{13}5}=\dfrac{12}{13}$
$\coth x=\dfrac1{\tanh x}=\dfrac{13}{12}$

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Ответ:

danny1234huang

04.08.2022

Mathematics

9/10 = 72/80 (multiply top and bottom by 8)

6/8 = 60/80 (multiply top and bottom by 10)

Therefore 9/10 is greater than 6/8.

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If cosh x = 13 5 and x > 0, find the values of the other hyperbolic functions at x.

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