Yes, 355÷113 is very close to π, but is not equal to π
So how does it get things 'right' for cos(355÷113), but not right for sin(355÷113)?
And why is the error of π-355÷113 exactly the same as the error of sin(355÷113)?
I sense some fuckiness of how they handle π...
The correct answer in degrees is cos(pi) = 0.99849714986386383364. The correct answer in radians is cos(pi) = -1 (exactly). Any calculator giving you cos(pi) = -1 is definitely in radians mode - and if you mean you're getting cos(pi) = exactly 1, and not 0.998, then that should never happen in any mode, unless it just has two digits of accuracy. Which I doubt any calculator with a 'cos' button has ever had.
For the record, if using sine, you should have sin(pi) = 0.05480366514878953089 if in degrees mode, or sin(pi) = 0 (exactly) if in radians mode.