Difference between revisions of "TrigExpand Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | ||
| − | ;TrigExpand | + | ;TrigExpand( <Expression> ) |
:Transforms a trigonometric expression into an expression using only simple variables as arguments. | :Transforms a trigonometric expression into an expression using only simple variables as arguments. | ||
:{{example|1=<code>TrigExpand[tan(x + y)]</code> gives <math>\frac{\frac{sin(x)}{cos(x)}+\frac{sin(y)}{cos(y)}} {1-\frac{sin(x)}{cos(x)} \cdot \frac{sin(y)}{cos(y)}} </math>.}} | :{{example|1=<code>TrigExpand[tan(x + y)]</code> gives <math>\frac{\frac{sin(x)}{cos(x)}+\frac{sin(y)}{cos(y)}} {1-\frac{sin(x)}{cos(x)} \cdot \frac{sin(y)}{cos(y)}} </math>.}} | ||
| − | ;TrigExpand | + | ;TrigExpand( <Expression>, <Target Function> ) |
:Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function. | :Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function. | ||
:{{example|1=<code>TrigExpand[tan(x + y), tan(x)]</code> gives <math>\frac{-tan(x) - tan(y)}{tan(x) tan(y) - 1}</math>.}} | :{{example|1=<code>TrigExpand[tan(x + y), tan(x)]</code> gives <math>\frac{-tan(x) - tan(y)}{tan(x) tan(y) - 1}</math>.}} | ||
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The following commands are only available in the [[File:Menu view cas.svg|link=|16px]] [[CAS View]]: | The following commands are only available in the [[File:Menu view cas.svg|link=|16px]] [[CAS View]]: | ||
| − | ;TrigExpand | + | ;TrigExpand( <Expression>, <Target Function>, <Target Variable> ) |
:Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and target variable. | :Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and target variable. | ||
:{{example|1=<code>TrigExpand[sin(x), sin(x), x/2]</code> gives <math>2cos \left( \frac{x}{2} \right) sin \left( \frac{x}{2} \right) </math>.}} | :{{example|1=<code>TrigExpand[sin(x), sin(x), x/2]</code> gives <math>2cos \left( \frac{x}{2} \right) sin \left( \frac{x}{2} \right) </math>.}} | ||
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| − | ;TrigExpand | + | ;TrigExpand( <Expression>, <Target Function>, <Target Variable>, <Target Variable> ) |
:Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and target variables. | :Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and target variables. | ||
:{{example|1=<code>TrigExpand[csc(x) - cot(x) + csc(y) - cot(y), tan(x), x/2, y/2]</code> gives <math>tan \left( \frac{x}{2} \right) +tan \left( \frac{y}{2} \right) </math>.}} | :{{example|1=<code>TrigExpand[csc(x) - cot(x) + csc(y) - cot(y), tan(x), x/2, y/2]</code> gives <math>tan \left( \frac{x}{2} \right) +tan \left( \frac{y}{2} \right) </math>.}} | ||
{{note|See also [[TrigSimplify Command]] and [[TrigCombine Command]].}} | {{note|See also [[TrigSimplify Command]] and [[TrigCombine Command]].}} | ||
Revision as of 17:17, 7 October 2017
- TrigExpand( <Expression> )
- Transforms a trigonometric expression into an expression using only simple variables as arguments.
- Example:
TrigExpand[tan(x + y)]gives \frac{\frac{sin(x)}{cos(x)}+\frac{sin(y)}{cos(y)}} {1-\frac{sin(x)}{cos(x)} \cdot \frac{sin(y)}{cos(y)}} .
- TrigExpand( <Expression>, <Target Function> )
- Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function.
- Example:
TrigExpand[tan(x + y), tan(x)]gives \frac{-tan(x) - tan(y)}{tan(x) tan(y) - 1}.
CAS Syntax
CAS syntaxes may show different results, depending on the selected output mode:
- Example:
TrigExpand[tan(x + y)]
in
Evaluate mode gives \frac{\frac{sin(x)}{cos(x)}+\frac{sin(y)}{cos(y)}} {1-\frac{sin(x)}{cos(x)} \cdot \frac{sin(y)}{cos(y)}}
in
Numeric mode gives \frac{sin(x) cos(y) + sin(y) cos(x)}{- sin(x) sin(y) +cos(x) cos(y) } .
The following commands are only available in the 
CAS View:
- TrigExpand( <Expression>, <Target Function>, <Target Variable> )
- Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and target variable.
- Example:
TrigExpand[sin(x), sin(x), x/2]gives 2cos \left( \frac{x}{2} \right) sin \left( \frac{x}{2} \right) .
- Example:
TrigExpand[sin(x)/(1+cos(x)), tan(x), x/2]gives tan \left( \frac{x}{2} \right).
- TrigExpand( <Expression>, <Target Function>, <Target Variable>, <Target Variable> )
- Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and target variables.
- Example:
TrigExpand[csc(x) - cot(x) + csc(y) - cot(y), tan(x), x/2, y/2]gives tan \left( \frac{x}{2} \right) +tan \left( \frac{y}{2} \right) .
Note: See also TrigSimplify Command and TrigCombine Command.
