Angle: \(\alpha\)

Trigonometric functions: \(\sin \alpha\), \(\cos \alpha\), \(\tan \alpha\)

- Sine squared

\({\sin^2}\alpha =\) \( \large\frac{{1 – \cos 2\alpha }}{2}\normalsize\) - Sine cubed

\({\sin^3}\alpha =\) \( \large\frac{{3\sin \alpha – \sin 3\alpha }}{4}\normalsize\) - Sine to the fourth power

\({\sin^4}\alpha =\) \( \large\frac{{\cos 4\alpha – 4\cos 2\alpha + 3}}{8}\normalsize\) - Sine to the fifth power

\({\sin^5}\alpha =\) \( \large\frac{{10\sin \alpha – 5\sin 3\alpha + \sin 5\alpha}}{16}\normalsize\) - Sine to the sixth power

\({\sin^6}\alpha =\) \( \large\frac{{10 – 15\cos 2\alpha + 6\cos 4\alpha – \cos 6\alpha}}{32}\normalsize\) - Cosine squared

\({\cos^2}\alpha =\) \( \large\frac{{1 + \cos 2\alpha }}{2}\normalsize\) - Cosine cubed

\({\cos^3}\alpha =\) \( \large\frac{{3\cos \alpha + \cos 3\alpha }}{4}\normalsize\) - Cosine to the fourth power

\({\cos^4}\alpha =\) \( \large\frac{{\cos 4\alpha + 4\cos 2\alpha + 3}}{8}\normalsize\) - Cosine to the fifth power

\({\cos^5}\alpha =\) \( \large\frac{{10\cos \alpha + 5\sin 3\alpha + \cos 5\alpha}}{16}\normalsize\) - Cosine to the sixth power

\({\cos^6}\alpha =\) \( \large\frac{{10 + 15\cos 2\alpha + 6\cos 4\alpha + \cos 6\alpha}}{32}\normalsize\) - Tangent squared

\({\tan^2}\alpha = {\large\frac{{{{\sin }^2}\alpha }}{{{{\cos }^2}\alpha}}\normalsize} =\) \( {\large\frac{{1 – \cos 2\alpha }}{{1 + \cos 2\alpha }}\normalsize}\) - Tangent cubed

\({\tan^3}\alpha = {\large\frac{{{{\sin }^3}\alpha }}{{{{\cos }^3}\alpha}}\normalsize} =\) \( {\large\frac{{3\sin \alpha – \sin 3\alpha }}{{3\cos \alpha + \cos 3\alpha}}\normalsize}\)