is there a way to return the current angle type (degree/radian) without actually changing that?

I want to make an if statement to warn users if they are in degrees instead of radians.
Sure, you can just do something like this:

If 5°=5 Then
Disp "DEG"
Disp "RAD"
To check for if a user is using degrees instead of radians, just look to see if the value is greater than a certain multiple of tau.

Or... just multiply by pi/180 if the answer is not a rational multiple of pi;.

Edit: oh instead just set K to 1 then if womp's code returns radians, or pi/180 if it returns degrees. Every time you have a degree, multiply it by K.
You should check if 1ʳ=1, which will be true in RADIAN mode but not in DEGREE or GRADIAN mode, if you specifically want to warn the user if not in radian mode. If you want them to not be in degree mode but either of the others is fine, you could instead check if 1°=1 like mr womp womp suggested. (& similarly, 1ᴳ=1 is the check for gradian mode specifically.) I think they added gradians later than the original TI-89, but you should account for it anyway in case people run your program on a TI-89 Titanium.

(There may also be another way to check by reading the mode settings directly, but that seems needlessly complicated.)
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