Simplifying a arc length problem

  • Thread starter hutchwilco
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  • #1

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Simplifying an arc length problem

I have L= Int(-2..2) sqrt(16*cosh(4*t)^2+9*sinh(4*t)^2+9)

and can use Maple to simplify this to sqrt(25*cosh(4*t)^2)
but I just can't see how that is done. (or how to get maple to show me the steps!)

Can anyone help by showing the steps, including any trig substitutions/identities used?
 
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Answers and Replies

  • #2
305
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try the definition of cosh and sinh in terms of exponentials (or use that to derive the hyperbolic equivalent of sin^2 + cos^2 = 1)
 
  • #3
Gib Z
Homework Helper
3,346
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[tex] 1+ \sinh^2 x = .....[/tex] so [tex] 9 + 9 \sinh^2 (4t) = ..................[/tex]?
 
  • #4
ah! thanks - i can't believe I didn't see that - it's only one step! I often have problems seeing the stripped down identities and applying them to problems which have other factors (eg 9 and 4t etc).
Thanks for the hint
 

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