# sinh(x) and cosh(x)

• June 13th 2011, 07:35 AM
Alexrey
sinh(x) and cosh(x)
Am I correct in saying that sinh(x) = 0 only when x = 0 and cosh(x) never equals 0?
• June 13th 2011, 07:37 AM
Prove It
Yes. To prove it, write $\displaystyle \sinh{x} = \frac{e^x - e^{-x}}{2}$, set it equal to 0 and solve for $\displaystyle x$. Also, set $\displaystyle \cosh{x} = \frac{e^x + e^{-x}}{2}$, and show that this is always positive.
• June 13th 2011, 09:37 AM
Alexrey
Thanks very much PI.