RE: Trig Error
- To: mathgroup@smc.vnet.net
- Subject: [mg11445] RE: [mg11396] Trig Error
- From: Ersek_Ted%PAX1A@mr.nawcad.navy.mil
- Date: Thu, 12 Mar 1998 01:33:44 -0500
Loren Dill wrote: ---------- |I discovered an error in the trigonometry functions of all places. | |The exact value of Cot [11/2 Pi] is zero, but Mathematica 3.0 gives |ComplexInfinity (!) for the nearly equivalent |Cot[17.2787595947438628115445386080397220812326`30.2181]. | |Has anyone else noticed similar trig errors? | |Loren Dill | Watch the precision of the output fall as the precision of the argument goes down. In[1]:= Cot[17.2787`16.]//InputForm Out[1]//InputForm= 0.00005959474393336246201506`10.5377 In[2]:= Cot[17.2787`8.]//InputForm Out[2]//InputForm= 0.000059594743933362`2.5377 In[3]:= Cot[17.2787`7.]//InputForm Out[3]//InputForm= 0.00005959474393336`1.5377 In[4]:= Cot[17.2787`6.]//InputForm Out[4]//InputForm= 0.0000595947439334`0.5377 In[5]:= Cot[17.2787`5.5]//InputForm Out[5]//InputForm= 0.000059594743933`0.0377 In[6]:= Cot[17.2787`5.465]//InputForm Out[6]//InputForm= 0.000059594743933`0.0027 In[7]:= Cot[17.2787`5.46] Out[7]= ComplexInfinity It seems the result in Out[7] would have had negative precision. This makes no sense, so Mathematica returns ComplexInfinity (just my guess). However, it seems to me Mathematica is relatively conservative when it determines how much precision the output has. I suppose they had to trade off execution time with better precision in the output. Also when they say the output has some amount of precision, they want to be absolutely certain the indicated precision is correct. Maybe the folks at Wolfram Research will have further comment. Ted Ersek