I've been reading about DCHP and ARP, and am confused about how your computer actually resolves the MAC address of the default gateway. The way I understand DHCP is this: When joining a network, your computer broadcasts a DHCP discover message to the machines on the LAN; the default gateway responds, telling you, among other things, the IP address it is giving you and its own IP address. But it doesn't respond with its MAC address (I checked in Wireshark).
My textbook says that your computer has an ARP table that just maps IP addresses to MAC addresses and how long those mappings remain valid. But say you haven't cached the MAC address of the router, either because the TTL expired or because you are first joining a network. My first instinct would be just sending out an ARP query, asking for the MAC address of the IP address given to you in the DHCP response. But that raises the question, why doesn't the DHCP acknowledgement just contain the default gateway's MAC address in addition to its IP address?