Maclaurin Series Derivatives – Useful Tables

Derivative Sine Cosine
f^{ \left( 0 \right) }\left( x \right) \sin { x } \cos { x }
f^{ \left( 1 \right) }\left( x \right) \cos { x } -\sin { x }
f^{ \left( 2 \right) }\left( x \right) -\sin { x } -\cos { x }
f^{ \left( 3 \right) }\left( x \right) -\cos { x } \sin { x }
f^{ \left( 4 \right) }\left( x \right) \sin { x } \cos { x }
f^{ \left( 5 \right) }\left( x \right) \cos { x } -\sin { x }
f^{ \left( 6 \right) }\left( x \right) -\sin { x } -\cos { x }
f^{ \left( 7 \right) }\left( x \right) -\cos { x } \sin { x }
f^{ \left( 8 \right) }\left( x \right) \sin { x } \cos { x }
f^{ \left( 9 \right) }\left( x \right) \cos { x } -\sin { x }
Derivative Sine Cosine
f^{ \left( 0 \right) }\left( 0 \right) 0.0 1.0
f^{ \left( 1 \right) }\left( 0 \right) 1.0 0.0
f^{ \left( 2 \right) }\left( 0 \right) 0.0 -1.0
f^{ \left( 3 \right) }\left( 0 \right) -1.0 0.0
f^{ \left( 4 \right) }\left( 0 \right) 0.0 1.0
f^{ \left( 5 \right) }\left( 0 \right) 1.0 0.0
f^{ \left( 6 \right) }\left( 0 \right) 0.0 -1.0
f^{ \left( 7 \right) }\left( 0 \right) -1.0 0.0
f^{ \left( 8 \right) }\left( 0 \right) 0.0 1.0
f^{ \left( 9 \right) }\left( 0 \right) 1.0 0.0

MACLAURIN SERIES EXPANSION:

taylor series expansion

SIN(X) FORMULA:

\sin { x } ={ x }-\frac { { x }^{ 3 } }{ 3! } +\frac { { x }^{ 5 } }{ 5! } -\frac { { x }^{ 7 } }{ 7! } +\frac { { x }^{ 9 } }{ 9! } -...

COS(X) FORMULA:

\cos { x } =1-\frac { { x }^{ 2 } }{ 2! } +\frac { { x }^{ 4 } }{ 4! } -\frac { { x }^{ 6 } }{ 6! } +\frac { { x }^{ 8 } }{ 8! } -...

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