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Article #98Re: Multiple angle help!!
From: Jim Nastos
Date: Sun, 15 Sep 1996 00:00
Date: Sun, 15 Sep 1996 00:00
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1559 bytes
Al (joiced@omen.com.au) wrote: : Would anyone please be able to shed some light on the above problem for me, : as i have reached a mental block on finding a totally perfect pattern or : rule to decide the expansion from simply sin nx or cos nx. Hmmm... okay... but I just hope this isn't for homework, or something. sin(nx) = n[cos(x)^(n-1)]*x*sin(x) - nC3(cos(x)^(n-3))*sin(x)^3 + nC5[cos(x)^(n-5)]*sin(x)^5 + ... for n = 2, 3, 4, ... and nCr = n!/[(r!)(n-r)!] cos(nx) = (cos(x))^n - nC2[cos(x)^(n-2)]*sin(x)^2 + nC4[cos(x)^(n-4)]*sin(x)^4 - ... with n and nCr being the same as stated above. -- Jim Nastos Mathematics '00 University of Waterloo
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f458d,d031a2c82abda88a X-Google-Attributes: gidf458d,public X-Google-Thread: 15dbc3,d031a2c82abda88a X-Google-Attributes: gid15dbc3,public X-Google-Thread: 1077c2,d031a2c82abda88a X-Google-Attributes: gid1077c2,public X-Google-Thread: 10d67e,d031a2c82abda88a X-Google-Attributes: gid10d67e,public X-Google-Thread: f86a3,d031a2c82abda88a X-Google-Attributes: gidf86a3,public From: cd467@torfree.net (Jim Nastos) Subject: Re: Multiple angle help!! Date: 1996/09/15 Message-ID: <Dxr2HE.3s4.0.bloor@torfree.net> X-Deja-AN: 180679139 references: <01bb9bf3$49e01100$1b5c0fcb@default> organization: Toronto Free-Net followup-to: alt.uu.math.misc,aus.mathematics,k12.ed.math,uk.education.maths,uwa.maths.general newsgroups: alt.uu.math.misc,aus.mathematics,k12.ed.math,uk.education.maths,uwa.maths.general