On each loop iteration the flag value changes sign, so it follows this pattern:
+1
-1
+1
-1
...
This has the effect of alternately adding or subtracting the following term:
+ (x^0)/factorial(0)
- (x^2)/factorial(2)
+ (x^4)/factorial(4)
- (x^6)/factorial(6)
...
This avoids the need to call two different plus and minus operators (but that would also be a perfectly viable approach).
