MandysNotes

Tuesday, 13 November 2012 18:03

Primitives of Trigonometric Functions

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

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

\[ \int {\color{Green}\tan}\ {z} ={ \ln} | {{\color{Purple}\sec}\ {z}} | = -{ \ln} | {{\color{Blue}\cos}\ {z}} | \]

\[ \int{{\color{orange}\csc}\ {z}} = {\ln} | {{\color{orange}\csc}\ {z} - {\color{Brown} \cot}\ {z} } | ={ \ln}\left| {{\color{Green}\tan}\ {\frac{z}{2}}} \right| = \frac{1}{2}{\ln}\left|\frac{1- {\color{Blue}\cos}\ {z}}{1 + {\color{Blue}\cos}\ {z}} \right| \]

\[ \int{ {\color{Purple} \sec}\ {z} } ={ \ln}{ \left| {\color{Purple}\sec}\ {z} + {\color{Green}\tan}\ {z} \right| } = {\ln} \left| {\color{Green}\tan}{\left( \frac{\pi}{4} + \frac{z}{2} \right)} \right| \]

\[ \int{ {\color{Brown} \cot}\ {z} } = - {\ln}{\left| {\color{orange}\csc}\ {z} \right|} = {\ln}\left| {\color{Goldenrod}\sin}\ {z} \right| \]

Read 3439 times Last modified on Friday, 14 February 2014 04:05

1 comment

  • Comment Link pravin Monday, 17 June 2013 10:40 posted by pravin

    where can i have free fonts of all trigonometric functions such as sin^2 x ,etc,etc...

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