Difference between revisions of "TrigExpand Command"
From GeoGebra Manual
(command syntax: changed [ ] into ( )) |
(Add example TrigExpand(sin(x)sin(x/3))) |
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: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>.}} | ||
+ | :It can also expand a product into a linear expression | ||
+ | :{{example|1=<code>TrigExpand(sin(x)sin(x/3))</code> gives <math>\frac{3}{2 \; x^{2}} \; cos \left( 2 \cdot \frac{x}{3} \right) - \frac{3}{2 \; x^{2}} \; cos \left( 4 \cdot \frac{x}{3} \right) </math>.}} | ||
;TrigExpand( <Expression>, <Target Function> ) | ;TrigExpand( <Expression>, <Target Function> ) |
Latest revision as of 08:54, 25 November 2020
- 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)}} .
- It can also expand a product into a linear expression
- Example:
TrigExpand(sin(x)sin(x/3))
gives \frac{3}{2 \; x^{2}} \; cos \left( 2 \cdot \frac{x}{3} \right) - \frac{3}{2 \; x^{2}} \; cos \left( 4 \cdot \frac{x}{3} \right) .
- 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:
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.