Richard Feynman found trigonometry notation to be ambiguous and confusing.
"If I had sin f, it looked like s×i×n×f"
So he decided to create his own notation. See below.
What do you think?pic.twitter.com/61ByeX7LMz
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I agree with his complaint whole-heartedly.
Are there any real world cases where one would need to do sin(sin(x))?
Why? I use that notation for logarithms and such too. Even for statistics operators like expectation, variance, bias, if any of those quantities are squared I write them with the operator, a 2 in the exponent, then the quantity I'm performing the operator on. It makes sense!
Also, squared or power of two literally means a quantity multiplied by itself. It doesn't mean a function (like sin) done to itself twice, that doesn't make sense.
sin² x is disgusting.
Either we need to get rid of sin^2 x or sin^{-1} x. Both can't stay. It causes my students a great deal of confusion.
I failed an exercise of my first exam at college because I asked the meaning of sin^2 and the prof told me sin sin
in any case, my fault for not knowing that!
Legit!
Gauss was right! No sin to write (sin x)^2
Guess we have struggled with this, god bless Wolfram and Mathematica, without whom a mathematical thesis would have been impossible, given our handwriting skills, especially me, myriad attempts were made around troff and nroff 
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