Difference between revisions of "TrigExpand Command"
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;TrigExpand( <Expression> ) | ;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 | + | :{{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( <Expression>, <Target Function> ) | ;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 | + | :{{example|1=<code>TrigExpand(tan(x + y), tan(x))</code> gives <math>\frac{-tan(x) - tan(y)}{tan(x) tan(y) - 1}</math>.}} |
==CAS Syntax== | ==CAS Syntax== | ||
CAS syntaxes may show different results, depending on the selected output mode: | CAS syntaxes may show different results, depending on the selected output mode: | ||
| − | :{{example|1=<code>TrigExpand | + | :{{example|1=<code>TrigExpand(tan(x + y))</code> <br/> in [[Image:Mode evaluate.svg|32px]] ''Evaluate'' mode 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> <br/> in [[Image:Mode numeric.svg|32px]] ''Numeric'' mode gives <math>\frac{sin(x) cos(y) + sin(y) cos(x)}{- sin(x) sin(y) +cos(x) cos(y) }</math> .}} |
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;TrigExpand( <Expression>, <Target Function>, <Target Variable> ) | ;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. | ||
| − | :{{ | + | :{{examples|1=<div> |
| − | : | + | :*<code>TrigExpand(sin(x), sin(x), x/2)</code> gives <math>2cos \left( \frac{x}{2} \right) sin \left( \frac{x}{2} \right) </math> |
| + | :*<code>TrigExpand(sin(x)/(1+cos(x)), tan(x), x/2)</code> gives <math>tan \left( \frac{x}{2} \right)</math>.</div>}} | ||
;TrigExpand( <Expression>, <Target Function>, <Target Variable>, <Target Variable> ) | ;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 | + | :{{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 10:01, 9 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.
- Examples:
TrigExpand(sin(x), sin(x), x/2)gives 2cos \left( \frac{x}{2} \right) sin \left( \frac{x}{2} \right)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.
