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

1. Apr 12, 2015

### ksukhin

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 $x=πn$

2. Apr 12, 2015

### Staff: Mentor

$sinh(x) = \frac{e^x - e^{-x}}{2}$
$cosh(x) = \frac{e^x + e^{-x}}{2}$
Clearly cosh(x) is never zero. It's pretty easy to find the zeroes of sinh(x).

3. Apr 12, 2015

### mathman

sinh(x)=0 when x=0.