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Trig Substitution

• To: mathgroup at smc.vnet.net
• Subject: [mg93434] Trig Substitution
• From: "Bruce Colletti" <bwcolletti at verizon.net>
• Date: Sat, 8 Nov 2008 03:57:57 -0500 (EST)

Re Mathematica 6.0.3 under WinXP.

 

Given a sum of (positive integer) powers of sin(t), I wish to cast (as much
as possible) the sum in terms of cos t, chiefly by substituting 1 - (cos
t)^2 for (sin t)^2 throughout.  The code below does this.

 

X=Sin[t]+Sin[t]^2+Sin[t]^3;

 

Y=Apply[List,X]/.{Sin[t]^n_?EvenQ:>Expand[(1-Cos[t]^2)^(n/2)],Sin[t]^n_:>Exp
and[(1-Cos[t]^2)^Quotient[n,2] Sin[t]]};

 

Apply[Plus,Y]

 

What is an easier way?  Thankx.

 

Bruce

 

• Follow-Ups:
  • Re: Trig Substitution
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>