Title: Multiple-Angle Formulas -- from Wolfram MathWorld
Open Graph Title: Multiple-Angle Formulas -- from Wolfram MathWorld
X Title: Multiple-Angle Formulas -- from Wolfram MathWorld
Description: For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. For sin(nx), sin(nx) = (e^(inx)-e^(-inx))/(2i) (1) = ((e^(ix))^n-(e^(-ix))^n)/(2i) (2) = ((cosx+isinx)^n-(cosx-isinx)^n)/(2i) (3) = sum_(k=0)^(n)(n; k)(cos^kx(isinx)^(n-k)-cos^kx(-isinx)^(n-k))/(2i) (4) = sum_(k=0)^(n)(n; k)cos^kxsin^(n-k)x(i^(n-k)-(-i)^(n-k))/(2i) (5) = sum_(k=0)^(n)(n;...
Open Graph Description: For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. For sin(nx), sin(nx) = (e^(inx)-e^(-inx))/(2i) (1) = ((e^(ix))^n-(e^(-ix))^n)/(2i) (2) = ((cosx+isinx)^n-(cosx-isinx)^n)/(2i) (3) = sum_(k=0)^(n)(n; k)(cos^kx(isinx)^(n-k)-cos^kx(-isinx)^(n-k))/(2i) (4) = sum_(k=0)^(n)(n; k)cos^kxsin^(n-k)x(i^(n-k)-(-i)^(n-k))/(2i) (5) = sum_(k=0)^(n)(n;...
X Description: For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. For sin(nx), sin(nx) = (e^(inx)-e^(-inx))/(2i) (1) = ((e^(ix))^n-(e^(-ix))^n)/(2i) (2) = ((cosx+isinx)^n-(cosx-isinx)^n)/(2i) (3) = sum_(k=0)^(n)(n; k)(cos^kx(isinx)^(n-k)-cos^kx(-isinx)^(n-k))/(2i) (4) = sum_(k=0)^(n)(n; k)cos^kxsin^(n-k)x(i^(n-k)-(-i)^(n-k))/(2i) (5) = sum_(k=0)^(n)(n;...
Opengraph URL: https://mathworld.wolfram.com/Multiple-AngleFormulas.html
Domain: mathworld.wolfram.com
| DC.Title | Multiple-Angle Formulas |
| DC.Creator | Weisstein, Eric W. |
| DC.Description | For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. For sin(nx), sin(nx) = (e^(inx)-e^(-inx))/(2i) (1) = ((e^(ix))^n-(e^(-ix))^n)/(2i) (2) = ((cosx+isinx)^n-(cosx-isinx)^n)/(2i) (3) = sum_(k=0)^(n)(n; k)(cos^kx(isinx)^(n-k)-cos^kx(-isinx)^(n-k))/(2i) (4) = sum_(k=0)^(n)(n; k)cos^kxsin^(n-k)x(i^(n-k)-(-i)^(n-k))/(2i) (5) = sum_(k=0)^(n)(n;... |
| DC.Date.Created | 2000-02-28 |
| DC.Date.Modified | 2008-06-05 |
| DC.Subject | 51N |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/Multiple-AngleFormulas.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| Last-Modified | 2008-06-05 |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_Multiple-AngleFormulas.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_Multiple-AngleFormulas.png |
| None | ie=edge |
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