When connecting to a projector, or another secondary display, you have the ability to adjust the resolution sent to that display. Go to your System Preferences, select Displays, under the Display tab choose Scaled to see a list of available resolutions.
The available resolutions in this list are abbreviated. To see more available resolutions, hold the Option key and click the word Scaled. More options will appear and you can choose from the extended list. Click "Okay" when prompted to keep the new selected resolution.