Category:Quintuple Angle Formula for Sine

From ProofWiki
Jump to navigation Jump to search
\(\ds \map \sin {5 \theta}\) \(=\) \(\ds 5 \sin \theta - 20 \sin^3 \theta + 16 \sin ^5 \theta\) Quintuple Angle Formulas/Sine
\(\ds \map \sin {5 \theta}\) \(=\) \(\ds \sin \theta \paren { \paren {2 \cos \theta}^4 - 3 \paren {2 \cos \theta}^2 + 1 }\) Sine of Integer Multiple of Argument/Formulation 1/Examples/Sine of Quintuple Angle
\(\ds \map \sin {5 \theta}\) \(=\) \(\ds \cos^5 \theta \paren {5 \tan \theta - 10 \tan^3 \theta + \tan^5 \theta}\) Sine of Integer Multiple of Argument/Formulation 2/Examples/Sine of Quintuple Angle
\(\ds \map \sin {5 \theta}\) \(=\) \(\ds \map \sin {\theta} + 2 \cos \theta \paren { \sin 4 \theta - \sin 2 \theta }\) Sine of Integer Multiple of Argument/Formulation 5/Examples/Sine of Quintuple Angle
\(\ds \map \sin {5 \theta}\) \(=\) \(\ds \map \sin {\theta} + 2 \sin \theta \paren { \cos 4 \theta + \cos 2 \theta }\) Sine of Integer Multiple of Argument/Formulation 7/Examples/Sine of Quintuple Angle
\(\ds \map \sin {5 \theta}\) \(=\) \(\ds \map \sin {4 \theta} \paren { 2 \cos \theta - \cfrac 1 {2 \cos \theta - \cfrac 1 {2 \cos \theta - \cfrac 1 {2 \cos \theta } } } }\) Sine of Integer Multiple of Argument/Formulation 8/Examples/Sine of Quintuple Angle
\(\ds \map \sin {5 \theta}\) \(=\) \(\ds \map \cos {4 \theta} \paren { 2 \sin \theta + \cfrac 1 {-2 \sin \theta + \cfrac 1 {2 \sin \theta + \cfrac 1 {-2 \sin \theta + \cfrac 1 {\map \sin {\theta} } } } } }\) Sine of Integer Multiple of Argument/Formulation 9/Examples/Sine of Quintuple Angle