This article provides trigonometry equation examples in LibreOffice Math. Below you can get the codes you can run in Math to show the equations. And you can download below the document files so you can study and change them. This article is a part of LibreOffice Math the series (Getting Started, Matrix, Integrals, Limits). I hope this article is helpful for teachers using LibreOffice at schools.
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How It Looks
Here you can see the code applied in both LibreOffice Math and Writer.
Example 1
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Code:
sin 0 = 0
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sin 30^o = 1 over 2
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sin 45^o = {1 over 2} sqrt{ 2 }
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sin 60^o = { 1 over 2 } sqrt{ 3 }
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sin 90^o = 1
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Example 2
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Code:
matrix {
cos 0^o #{}={}# 0 ##
cos 30^o #{}={}# {1 over 2} sqrt{3} ##
cos 45^o #{}={}# {1 over 2} sqrt{2} ##
cos 60^o #{}={}# {1 over 2} ##
cos 90^o #{}={}# 0
}
Example 3
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Code:
matrix{
%itheta # 0 # 30^o # 45^o # 60^o # 90^o ##
{} # {}# {} # {} # {} # {} ##
sin # 0 # {1 over 2} # {1 over 2} sqrt{2} # {1 over 2} sqrt{3} # 1 ##
cos # 1 # {1 over 2} sqrt{3} # {1 over 2} sqrt{2} # 1 over 2 # 0 ##
tan # 0 # {1 over 3} sqrt{3} # 1 # sqrt{3} # U
}
Example 4
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Code:
Trigonometric functions:
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tan %itheta = { {sin %itheta} over {cos %itheta} }
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sec %itheta = 1 over { cos %itheta }
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csc %itheta = 1 over { sin %itheta }
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cot %itheta = 1 over { tan %itheta } = { cos %itheta } over { sin %itheta }
Example 5
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Code:
Invers functions:
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sin( arcsin x ) = x, for lline x rline <= 1
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arcsin( sin x ) = x, for lline x rline <= {%pi over 2}.
Example 6
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Code:
Pythagorean identity:
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sin^2 %itheta + cos^2 %itheta = 1
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sin %itheta = +-{ sqrt{1 - cos^2 %itheta} }
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cos %itheta = +-{ sqrt{1 - sin^2 %itheta} }
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Example 7
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Code:
sin( %alpha +- %beta ) = sin %alpha cos %beta +- cos %alpha sin %beta
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cos( %alpha +- %beta ) = cos %alpha cos %beta -+ sin %alpha sin %beta
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tan( %alpha +- %beta ) = { tan %alpha +- tan %beta } over { 1 -+ tan %alpha tan %beta }
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Example 8
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Code:
double angle formulae:
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sin( 2 %itheta ) = 2 sin %itheta cos %itheta
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cos( 2 %itheta ) = cos^2 %itheta - sin^2 %itheta = 2 cos^2 %itheta - 1 = 1 - 2 sin^2 %itheta = { 1 - tan^2 %itheta } over { 1 + tan^2 %itheta }
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tan( 2 %itheta ) = { 2 tan %itheta } over { 1 - tan^2 %itheta }
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Example 9
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Code:
sin %alpha sin %beta = 1 over 2 [ cos(%alpha - %beta) - cos(%alpha + %beta) ]
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cos %alpha cos %beta = 1 over 2 [ cos(%alpha - %beta) + cos(%alpha + %beta) ]
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Example 10
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Code:
sin %alpha + sin %beta = 2 sin ( {%alpha + %beta} over 2 ) cos ( {%alpha - %beta} over 2 )
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sin %alpha - sin %beta = 2 cos ( {%alpha + %beta} over 2 ) sin ( {%alpha - %beta} over 2 )
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Download Sample Documents
Here I provide the LibreOffice Math & Writer document files so you can view and edit all trigonometry equations as you wish. I licensed them under CC BY-SA.
LibreOffice Math (.odf)
LibreOffice Writer (.odt)