Sextuple Angle Formulas

Theorem

Sextuple Angle Formula for Sine

$\dfrac {\sin 6 \theta} {\sin \theta} = 32 \cos^5 \theta - 32 \cos^3 \theta + 6 \cos \theta$

Sextuple Angle Formula for Cosine

$\cos 6 \theta = 32 \cos^6 \theta - 48 \cos^4 \theta + 18 \cos^2 \theta - 1$

Sextuple Angle Formula for Tangent

$\tan 6 \theta = \dfrac { 6 \tan \theta - 20 \tan^3 \theta + 6 \tan^5 \theta } { 1 - 15 \tan^2 \theta + 15 \tan^4 \theta - \tan^6 \theta }$

where $\sin, \cos, \tan$ denote sine, cosine and tangent respectively.

Also see

• Quintuple Angle Formulas