Hyperbolic Sine of Zero is Zero

Theorem

$\map \sinh 0 = 0$

where $\sinh$ denotes the hyperbolic sine.

Proof

\(\ds \map \sinh 0\)

\(=\)

\(\ds \dfrac {e^0 - e^{-0} } 2\)

Definition of Hyperbolic Sine

\(\ds \)

\(=\)

\(\ds \dfrac {1 - 1} 2\)

Definition of Integer Power

\(\ds \)

\(=\)

\(\ds 0\)

$\blacksquare$

Also see

• Hyperbolic Cosine of Zero is One‏‎