Elementary analytic functions in $VT{C}^0$

It is known that rational approximations of elementary analytic functions (exp, log, trigonometric, and hyperbolic functions, and their inverse functions) are computable in the weak complexity class ${\mathrm{T}\mathrm{C}}^0$. We show how to formalize the construction and basic properties of these functions in the corresponding theory of bounded arithmetic, ${\mathsf{V}\mathsf{T}\mathsf{C}}^0$.