Difference between revisions of "TrigExpand Command"
From GeoGebra Manual
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| − | <noinclude>{{Manual Page|version=4.2}}</noinclude> | + | <noinclude>{{Manual Page|version=4.2}}</noinclude> |
{{command|cas=true|function}} | {{command|cas=true|function}} | ||
;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[tan(x + y)]</code> gives <math>\frac{cos(x) sin(y) + cos(y) sin(x)}{cos(x) cos(y) - sin(x) sin(y)}</math>.}} | :{{example|1=<code>TrigExpand[tan(x + y)]</code> gives <math>\frac{cos(x) sin(y) + cos(y) sin(x)}{cos(x) cos(y) - sin(x) sin(y)}</math>.}} | ||
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;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[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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==CAS Syntax== | ==CAS Syntax== | ||
;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[tan(x + y)]</code> gives <math>\frac{cos(x) sin(y) + cos(y) sin(x)}{cos(x) cos(y) - sin(x) sin(y)}</math>.}} | :{{example|1=<code>TrigExpand[tan(x + y)]</code> gives <math>\frac{cos(x) sin(y) + cos(y) sin(x)}{cos(x) cos(y) - sin(x) sin(y)}</math>.}} | ||
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;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[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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;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 tagret variable. | :Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and tagret variable. | ||
:{{example|1=<code>TrigExpand[sin(x), sin(x), x/2]</code> gives <math>2cos(\frac{x}{2})sin(\frac{x}{2})</math>.}} | :{{example|1=<code>TrigExpand[sin(x), sin(x), x/2]</code> gives <math>2cos(\frac{x}{2})sin(\frac{x}{2})</math>.}} | ||
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;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[csc(x) - cot(x) + csc(y) - cot(y), tan(x), x/2, y/2]</code> gives <math>tan(\frac{x}{2})+tan(\frac{y}{2})</math>.}} | :{{example|1=<code>TrigExpand[csc(x) - cot(x) + csc(y) - cot(y), tan(x), x/2, y/2]</code> gives <math>tan(\frac{x}{2})+tan(\frac{y}{2})</math>.}} | ||
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{{note|See also [[TrigSimplify Command]] and [[TrigCombine Command]].}} | {{note|See also [[TrigSimplify Command]] and [[TrigCombine Command]].}} | ||
Revision as of 11:39, 21 December 2012
- TrigExpand[ <Expression> ]
- Transforms a trigonometric expression into an expression using only simple variables as arguments.
- Example:
TrigExpand[tan(x + y)]gives \frac{cos(x) sin(y) + cos(y) sin(x)}{cos(x) cos(y) - sin(x) sin(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
- TrigExpand[ <Expression> ]
- Transforms a trigonometric expression into an expression using only simple variables as arguments.
- Example:
TrigExpand[tan(x + y)]gives \frac{cos(x) sin(y) + cos(y) sin(x)}{cos(x) cos(y) - sin(x) sin(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}.
- 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 tagret variable.
- Example:
TrigExpand[sin(x), sin(x), x/2]gives 2cos(\frac{x}{2})sin(\frac{x}{2}).
- 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(\frac{x}{2})+tan(\frac{y}{2}).
Note: See also TrigSimplify Command and TrigCombine Command.
