Disagreement between two pilots of a B737 on how to program a fix in their FMS defined by a radial and distance led to a track deviation.

Narrative

We were proceeding direct SXC direct SNA. We were then given the clearance to proceed direct to the BENET 287 degree radial; 55 DME fix; direct BENET as filed. Next we were given clearance pilots discretion descend to FL240. I verbally verified the programming necessary for the FMC with the Captain; that the point would have to be constructed in the FIX page; and then entered on the LEGS page. As I was programming it my Captain was insistent that it needed to be entered as the reciprocal of 287 (107/55). I typed in what he said instead of what I thought should be entered; and the depicted flight path on the CDU did not make sense. We didn't execute the course change; as it looked erroneous. We called and verified the clearance of direct to the BENET 287 @ 55 DME; direct BENET. The Captain was positive the fix was programmed correctly and that something else must be wrong. The Captain reentered the fix information on the FIX page and reentered it on the LEGS page with the same result. The programming didn't seem right to me and I verbalized as much; as I thought creating the fix was straight-forward (287/55); but he was insistent. I had rarely had to build a fix in the FMC before; and since the Captain was so sure of himself I began to doubt myself on the programming. In the time span of us trying to get the clearance programmed; the Captain said; 'I know where they want us; just go heading about twenty left of our current heading'. Just as I engaged heading mode and began our pilot discretion descent ATC called; stating; you look off course; for traffic cancel descent clearance maintain FL410 and turn to heading XXX. We complied with their instructions; and in aggravation I finally reprogrammed the FMC as I had felt was the correct method (287/55) and the point came up correctly. The Captain had an exchange with ATC and then we were re cleared to the BENET 287/55 DME. The Captain then started apologizing profusely to me for confusing the issue; that he was confused about how to program the fix himself and that I was right in the first place. Contributing to the error situation was the Captain's confusion on how to program the FMC; my own self-doubt of my abilities (fostered from the cockpit dynamics between the Captain and I from the last two days of our trip together); our failure to request a heading immediately to get us in the right direction while we worked on the FMC programming and lastly lack of adherence to our company standard operation procedures regarding the duties of pilot flying/pilot monitoring. I was the pilot flying (with autopilot engaged) and as such should have been programming and executing changes in the FMC.