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
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