Based on your video on the ambiguity of superscripts in trigonometry functions () I started a Change.org petition to reduce this ambiguity:

## math for fun

To see this working, head to your live site.

Dec 27, 2021

# Petition to change trigonometry function notation with regards to superscript

Petition to change trigonometry function notation with regards to superscript

8 comments

0

It means 1/(tan x)^2. The -1 exponent for inverse trig functions is here to stay whether you like it or not. It's just too ingrained in the global culture. If you want to express 1/tan(x) then (tan x)^-1 is about your only option. Also the -1 notation is used for a the general representation for "f inverse" that goes well beyond just the trig functions. Some use "arc" specifically for trig to avoid the confusion and that's about as good as you are going to get. I think you are just wasting your time as no petition is likely to have any real acceptance in the world wide mathematics community.

I am not against the tan^-1(x) notation. It makes sense to me. I do have issues with the tan^2(x) notation, because it makes tan^-2(x) ambiguous. In my opinion tan(x)^2 should be tanx*tanx and tan^2(x) should be tan(tanx)

Well, I have never seen a shortcut for tan[tan(x)], so I think you are alone on that one. Good luck trying to change that. The notation , for example, in sin^2(x) + cos^2(x) = 1, is here to stay.

f(f(x)) written as f^2(x) is just never going to happen.

I forgot that it's indeed not written as f^2(x) but as f_2(x), as done in the numberphile video of tree(3) vs

Don't get me wrong, I am sympathetic to your irritation and do agree that the -1 notation for inverse is a pain. Life soldiers on. Happy New Year.

Happy new year! It was a half serious, half joke kinda petition that I didn't expect getting anywhere anyways. You can't really change all the papers and books that are already out there, now can you?

One the one hand, that notation seems okay for the most part. But I don't see f^2(x) taking over f(f(x)).

On the other hand, is one of the most useless websites I've ever seen.

Oh definitely. If I really wanted to see if it could be changed, I'd try talking to professional/academic mathematicians in person and see where, going forward, they'd see themselves using it and where they see potential issues with the idea, like how would you prevent confusion in the short term in academic papers, how do you transition to the new notation in math text books, how do you deal with existing papers, both digital and written, etc. And even then, due to the history of use, it still probably wouldn't be changed. I feel like nothing short of a time machine could change this notation :D