An estimate for dish beamwidth is Bw = 21900 / (F * D)
Where F is the frequency in MHz and D is the diameter in Meters.
So, for your 1.2M dish at 4000 MHz, the beamwidth would be about 4.6 degrees.
Note that this formula calculates about 1.8 degrees for your 10-foot dish.
If you are using that 1.2M dish in the Ku band at 12000MHz the beamwidth would be about 1.5 degrees