MandysNotes

Trigonometric Formulae

Trigonometric Formulae (4)

Tuesday, 13 November 2012 18:53

Derivatives of Trigonometric Functions

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\[ \frac{d}{dx}{ \color{Goldenrod}\sin}\ {z} = {\color{Blue}\cos}\ {z} \]

 

\[ \frac{d}{dx}{\color{Blue} \cos}\ {z} = -{\color{Goldenrod} \sin}\ {z} \]

Tuesday, 13 November 2012 18:03

Primitives of Trigonometric Functions

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\[ \int{ \color{Goldenrod}\sin}\ {z} = - {\color{Blue}\cos}\ {z} \]

\[ \int{\color{Blue} \cos}\ {z} ={\color{Goldenrod} \sin}\ {z} \]

Tuesday, 13 November 2012 19:19

Addition Formulae

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\[ {\color{Goldenrod}\sin}\ \left( {\color{MidnightBlue}z_{1}} + {\color{MidnightBlue}z_{2}} \right) = {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z_{1}} \ {\color{Blue}\cos}\ {\color{MidnightBlue}z_{2}} \ + \ {\color{Blue}\cos}\ {\color{MidnightBlue}z_{1}}\ {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z_{2}} \ \]


\[ {\color{Blue}\cos}\ \left( {\color{MidnightBlue}z_{1}} + {\color{MidnightBlue}z_{2}} \right) = {\color{Blue}\cos}\ {\color{MidnightBlue}z_{1}} \ {\color{Blue}\cos}\ {\color{MidnightBlue}z_{2}} \ - \ {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z_{1}}\ {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z_{2}} \ \]

Tuesday, 13 November 2012 19:13

Half-Angle Formulae

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\[ { {\color{Goldenrod}\sin}\ \frac{{\color{MidnightBlue}z} }{2} } = \pm \left( \frac{1- {\color{Blue}\cos}\ {\color{MidnightBlue}z} }{2} \right)^{\frac{1}{2} } \]

\[ { {\color{Blue}\cos}\ \frac{{\color{MidnightBlue}z} }{2} } = \pm \left( \frac{1+ {\color{Blue}\cos}\ {\color{MidnightBlue}z} }{2} \right)^{\frac{1}{2} } \]

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