formula

$\begin{split} v_{I} &= v_{AM} \times cos(\omega_c t)\\ &= V_c \cdot cos(\omega_ct+\phi_c)\cdot cos(\omega_c t)\cdot(1+m\cdot cos(\omega_st+\phi_s))\\ v_{Q} &= v_{AM} \times cos(\omega_c t+{\pi\over2})\\ &= V_c \cdot cos(\omega_ct+\phi_c)\cdot cos(\omega_c t+{\pi\over2})\cdot(1+m\cdot cos(\omega_st+\phi_s))\\ \end{split}$