\begin{align} G_Y(u,v)&=F[g_Y(x,y)]\\ &=AF[sin(2\pi(u_vx+v_vy))]+F[c]+F[(Asin(2\pi(u_vx+v_vy))+c)cos(\Delta\varphi_Y(x,y))]\\ &=c\delta(u,v)+\frac{A[\delta(u-u_v,v-v_v)-\delta(u+u_v,v+v_v)]}{2i}+\frac{A[\delta(u-u_v,v-v_v)-\...