MandysNotes

Tuesday, 13 November 2012 19:13

Half-Angle Formulae

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

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


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


\[ { = \frac{1- {\color{Blue}\cos}\ {\color{MidnightBlue}z} }{ {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z} } } { = \frac { {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z} } {1\ + \ {\color{Blue}\cos}\ {\color{MidnightBlue}z} } } \]

Read 1828 times Last modified on Wednesday, 12 February 2014 16:43
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