The GPS $($Global Positioning System$)$ satellites are approximately $5\mathrm{.}18$ mm across and transmit two low$-$power signals, one of which is at $1575\mathrm{.}42$ MHzMHz $($in the UHF band$).$ In a series of laboratory tests on the satellite, you put two $1575\mathrm{.}42$ MHzMHz UHF transmitters at opposite ends of the satellite. These broadcast in phase uniformly in all directions. You measure the intensity at points on a circle that is several hundred meters in radius and centered on the satellite. You measure angles on this circle relative to a point that lies along the centerline of the satellite $($that is$,$ the perpendicular bisector of a line which extends from one transmitter to the other$).$ At this point on the circle, the measured intensity is $2\mathrm{.}00$ W$/$m$2$W$/$m$2.$

At how many other angles in the range $0<$$<900<$$<90$ is the intensity also $2\mathrm{.}00$ W$/$m$2$W$/$m$2?$

Find the four smallest $($positive$)$ angles in the range $0<$$<900<$$<90$ for which the intensity is $2\mathrm{.}00$ W$/$m$2$W$/$m$2.$

What is the intensity at a point on the circle at an angle of $4\mathrm{.}95$ from the centerline?