# LibreOffice Math: Trigonometry Equation Examples

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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

Picture:

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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