Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- To: mathgroup at smc.vnet.net
- Subject: [mg104639] Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Thu, 5 Nov 2009 03:52:27 -0500 (EST)
- References: <hce437$r4t$1@smc.vnet.net> <hcgmni$cpe$1@smc.vnet.net> <hcone9$100$1@smc.vnet.net>
On 2009.11.03. 8:51, Lawrence Teo wrote:
> Hi all,
>
> Thanks for the insight. So Simplify[] in Mathematica is right.
> But why I observe small delta if I subtract the two expressions with // N?
> Is it because of machine precision related limitation?
>
> a = Cos[x]^2 - Sin[x]^2
> b = Cos[x]^4 - Sin[x]^4
> Table[a - b, {x, -10, 10}] // N
>
It's because of rounding errors.
http://mathworld.wolfram.com/RoundoffError.html
Try this instead of Table:
Plot[Cos[x]^2 - Sin[x]^2 - (Cos[x]^4 - Sin[x]^4), {x, 0, 2 Pi}]