Find the unit tangent vector T$($t$).$

r$($t$)=$ e$5$t$$i $+$ cos$($t$)$j $$ sin$(4$t$)$k$,$P$(1,1,0)$

T$(0)=$

Find a set of parametric equations for the tangent line to the space curve at point P$.($Enter your answers as a comma$-$separated list of equations. Use t for the variable of parameterization.$)$