\[sin x \rightarrow i \: sinh x\]
\[cos x \rightarrow cosh x\]
\[tan x \rightarrow i \: tanh x\]
where
\[i=\sqrt{-1}\]
.Example:
\[cos 2x=cos^2x-sin^2x\]
becomes\[cosh2x=(coshx)^2-(i \: sinhx)^2=cosh^2x-(-sinh^2x)=cosh^2x+sinh^2x\]
Transforming Trigonometric Identies From Trigonometric to Hyperbolic Form
We can rewrite trigonometric identifies as hyperbolic identities using the transformation
where
Example:
where
Example: