monotonic decrease of sin (paradise version)

[Olivier Gerard]

At 18:53 +0200 99.04.19, vdmcc wrote:


->Neil,
->for what it's worth :
->----------------------------------------------------------------------------
->Sin[n] decreases monotonically to 0 :
->
->z={};current=1;
->Timing[Do[
->    If[If[(t=Sin[n])>0,t,1]<current,AppendTo[z,current=t ]],{n,105000 }]]
->
->{Sin[1],Sin[3],Sin[44],Sin[311],Sin[377],Sin[688],Sin[710],Sin[103638],
->  Sin[104703]}
->----------------------------------------------------------------------------
->
->Cos[n] decreases monotonically to -1 :
->z={};current=1;
->Timing[Do[If[Cos[n]<current,AppendTo[z,current=Cos[n]]],{n,105000}]]
->
->{Cos[1],Cos[2],Cos[3],Cos[22],Cos[355],Cos[104348]}
->----------------------------------------------------------------------------
->
->Abs[Tan[n]] decreases monotonically to 0 :
->z={};current=1;
->Timing[Do[
->    If[Abs[Tan[n]]<current,AppendTo[z,current=Abs[Tan[n]]]],{n,105000}]]
->{-Tan[3],Tan[22],-Tan[333],Tan[355],-Tan[103993],Tan[104348]}
->----------------------------------------------------------------------------

So, I was too short of a few thousands, for the next term in the sparse cases.
One should always have one's best computer handy, but my portable is old now.

->So let's be carefull with Gerard's early generalisations (;-))
->

Wouter, I was considering decrease to 0 and not to -1.


Olivier