Dr.Peterson, the reason why the tangent is undefined there is because it is where cos(x) equates to 0, and that cos function is used as a denominator in the tan function, and anything divided by 0 is undefined. Following this logic, the area that is undefined should be a single value, not a gap as I found. As for the calculator's limitations, I'm not entirely sure exactly how it is related to this problem, but I have considered this and eliminated it as a possibility. If it were the problem, then this number would have been something more round like 0.00...01. Also, the way I came to this number was by entering the maximum number in each digit that would still be undefined, therefore resulting in a number right at the border of where it is defined and undefined. I then multiplied that result by 2 to account for me starting at the center rather than the leftmost side of the gap, and that is how I got that number. From this, I have no variables to work with to see where the number originated from, and I feel that it is too specific of a number to have something to do with how the calculator functions.
JeffM, because of how specific it is, I don't think that it has anything to do with the program itself as said before. On top of this, if the calculator had seen this as an error, it wouldn't have sent the tan function in the first place because of how it works, so it can't be an error in the function. As for me calling the number odd, I was referring to how I couldn't trace it back to any known variables.
Also, sorry if I'm being a bit persistent on how the calculator works, I just don't believe it has anything to do with it.