Re: Sqrt[Sin^2(x)]=Sin(x)....????
- To: mathgroup at smc.vnet.net
- Subject: [mg16547] Re: [mg16329] Sqrt[Sin^2(x)]=Sin(x)....????
- From: "Dale Horton" <daleh>
- Date: Tue, 16 Mar 1999 04:00:19 -0500
- Organization: Wolfram Research, Inc.
- References: <7c58ve$7m8@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
a is only treu if a is a non-negative Real. Abs[a] is only true if a is Real. In general, Sqrt[a^2] is the only correct result. This why Mathematica leaves it unevaluated. PowerExpand is for people who don't want to mess with these issues. "PowerExpand also converts (a^b)^c to a^(b c) The transformations made by PowerExpand are correct in general only if c is an integer or a and b are positive real numbers. " In this case, b is 2 and c is 1/2. -Dale Ranko Bojanic wrote in message <7c58ve$7m8 at smc.vnet.net>... > > >The result returned by Mathematica > >In[1]:= Sqrt[a^2]//PowerExpand >Out[1]= a > >is clearly correct only if a is a nonnative number. >The only correct answer should be > >In[2]:= Sqrt[a^2]//PowerExpand >Out[2]= Abs[a] > >Regards, >Ranko > >> Alessandro Agresti <agresti at fi.infn.it> schrieb: > >>> Can I get the following result: >>> Sqrt[Sin^2(x)]=Sin(x) ??? >>> If so, how?? >>> Thanks You for Your BIG help. >>> Alessandro Agresti > >> Alessandro, > >> Mathematica knows, that this isn't always true. But you can use >> PowerExpand to get what you want: > >> In[1]= Sqrt[Sin[x]^2]//PowerExpand >> Out[1]= Sin[x] > >> es gruesst >> Peter > >> In a message dated 3/5/99 8:09:48 AM, agresti at fi.infn.it writes: > >>> Can I get the following result: >>> Sqrt[Sin^2(x)]=Sin(x) ??? >>> If so, how?? > >> Alessandro, > >> You have the exponent in the wrong position > >> Sqrt[Sin[x]^2] // PowerExpand >> Sin[x] > >> Bob Hanlon > >> Alessandro, >> let's hope you know what you are doing. > >> In[1]:= PowerExpand[Sqrt[Sin[x]^2] == Sin[x]] >> Out[1]= True > >> Jurgen > >> Alessandro Agresti wrote: >> >>> Can I get the following result: >>> Sqrt[Sin^2(x)]=Sin(x) ??? >>> If so, how?? >>> Thanks You for Your BIG help. >>> Alessandro Agresti > > >