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[tan(x + y)]</code> gives <math>\frac{cos(x) sin(y) | + | :{{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> ] | ||
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==CAS Syntax== | ==CAS Syntax== | ||
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+ | :{{example|1=<code>TrigExpand[tan(x + y)]</code> <br/> in mode [[Image:Mode evaluate.svg|32px]] Evaluate 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 mode [[Image:Mode numeric.svg|32px]] Numeric gives <math>\frac{sin(x) cos(y) + sin(y) cos(x)}{- sin(x) sin(y) +cos(x) cos(y) }</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]]: | ||
Revision as of 00:50, 29 December 2015
- 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
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.