Trivial solution for cosh(x)=0 and sinh(x)=0

  • Thread starter ksukhin
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  • #1
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I'm doing Sturm-Loiuville problems and I need to find the eigenvalues for λ

I'm having difficulty understanding the trivial solutions for the hyperbolic sin and cos when they equal 0.

I know that cos(x)=0 when ##x= π/2 + πn = (2n+1)π/2##
sin(x) = 0 when ##x=πn##

What about cosh(x) and sinh(x)? Please help
 

Answers and Replies

  • #2
34,514
6,200
I'm doing Sturm-Loiuville problems and I need to find the eigenvalues for λ

I'm having difficulty understanding the trivial solutions for the hyperbolic sin and cos when they equal 0.

I know that cos(x)=0 when ##x= π/2 + πn = (2n+1)π/2##
sin(x) = 0 when ##x=πn##

What about cosh(x) and sinh(x)? Please help
##sinh(x) = \frac{e^x - e^{-x}}{2}##
##cosh(x) = \frac{e^x + e^{-x}}{2}##
Clearly cosh(x) is never zero. It's pretty easy to find the zeroes of sinh(x).
 
  • #3
mathman
Science Advisor
7,889
460
sinh(x)=0 when x=0.
 

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