Re: Q: ArcTan[ Tan[ x ] ] = x

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1956] Re: Q: ArcTan[ Tan[ x ] ] = x*From*: pehowland at taz.dra.hmg.gb ()*Date*: Sat, 26 Aug 1995 00:10:39 -0400*Organization*: Defence Research Agency

In article <DDuMDu.Joy at wri.com>, elsner at avalon.msfc.nasa.gov (Ron Elsner) writes: |>Suppose I really want Mma to set ArcTan[ Tan[ x ] ] = x, or |>ArcSin[ Sin[ x ] ] = x. How do I do this? Hmm. Mathematica appears particularly stubborn over this one. I guess the mathematicians amongst us would argue that, strictly speaking, ArcSin[Sin[x]] =!= x, but rather ArcSin[Sin[x]] === x + (2 n Pi), due to the periodicity of the trig functions. However, it does seem that in certain circumstances it would be nice to be able to ignore this mathematical niceity. Anyway, the two obvious approaches are Simplify[expr, Trig->True] and <<Algebra`Trigonometry` TrigReduce[expr] but neither of these work, so I guess the only approach is to teach Mathematica some not-strictly-correct mathematics: In[1] := BadTrigRules = {ArcSin[Sin[a_]]->a, ArcTan[Tan[a_]]->a}; In[2] := ArcSin[Sin[x]] /. BadTrigRules Out[2] := x which forces the answer for you. You could write your own Simplify function that did this sort of thing first, and then applied Mathematica's built in Simplify fuction. It might be nice, however, for Mathematica's trig functions to have an option like "IgnorePeriodicity->True", or something, to force the above behaviour. Paul Howland Defence Research Agency UK