TrigExpand Command
From GeoGebra Manual
- 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.