Difference between revisions of "TrigCombine Command"

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(add TrigCombine[sin(x)+cos(x)] and TrigCombine[sin(x)+cos(x),sin(x)] examples)
m (add TrigCombine[sin(p) + cos(p), sin(x)], LaTeX tidying)
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;TrigCombine[ <Expression> ]
 
;TrigCombine[ <Expression> ]
 
:Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables.
 
:Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables.
−
:{{example|1=<code>TrigCombine[sin(x) cos(3x)]</code> gives <math>\frac{sin(4x)-sin(2x)}{2}</math>.}}
+
:{{example|1=<code>TrigCombine[sin(x) cos(3x)]</code> gives <math>{\frac{1}{2} \; \operatorname{sin} \left( 4 \; x \right) - \frac{1}{2} \; \operatorname{sin} \left( 2 \; x \right)}</math>.}}
−
:{{example|1=<code>TrigCombine[sin(x)+cos(x)]</code> gives <math> \mathbf{\sqrt{2} \; \operatorname{cos} \left( x - \frac{1}{4} \; \pi \right)} </math>.}}
+
:{{example|1=<code>TrigCombine[sin(x) + cos(x)]</code> gives <math> {\sqrt{2} \; \operatorname{cos} \left( x - \frac{1}{4} \; \pi \right)} </math>.}}
 
;TrigCombine[ <Expression>, <Target Function> ]
 
;TrigCombine[ <Expression>, <Target Function> ]
 
:Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables, preferring the given target function.
 
:Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables, preferring the given target function.
−
:{{example|1=<code>TrigCombine[sin(x)+cos(x),sin(x)]</code> gives <math> \mathbf{\sqrt{2} \; \operatorname{sin} \left( x + \frac{1}{4} \; \pi \right)} </math>.}}
+
:{{example|1=<code>TrigCombine[sin(x) + cos(x), sin(x)]</code> gives <math> {\sqrt{2} \; \operatorname{sin} \left( x + \frac{1}{4} \; \pi \right)} </math>.}}
  
 
==CAS Syntax==
 
==CAS Syntax==
 
;TrigCombine[ <Expression> ]
 
;TrigCombine[ <Expression> ]
 
:Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables.
 
:Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables.
−
:{{example|1=<code>TrigCombine[sin(x) cos(3x)]</code> gives <math>\frac{sin(4x)-sin(2x)}{2}</math>.}}
+
:{{example|1=<code>TrigCombine[sin(p) cos(3p)]</code> gives <math>{\frac{1}{2} \; \operatorname{sin} \left( 4 \; p \right) - \frac{1}{2} \; \operatorname{sin} \left( 2 \; p \right)}</math>.}}
  
 
;TrigCombine[ <Expression>, <Target Function> ]
 
;TrigCombine[ <Expression>, <Target Function> ]
 
:Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables, preferring the given target function.
 
:Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables, preferring the given target function.
−
:{{example|1=<code>TrigCombine[(tan(p) + tan(q)) / (1 - tan(p) tan(q)), tan(x)]</code> gives ''tan(p + q)''.}}
+
:{{example|1=<code>TrigCombine[sin(p) + cos(p), sin(x)]</code> gives <math> {\sqrt{2} \; \operatorname{sin} \left( p + \frac{1}{4} \; \pi \right)} </math>.}}
  
 
{{note|See also [[TrigExpand Command]] and [[TrigSimplify Command]].}}
 
{{note|See also [[TrigExpand Command]] and [[TrigSimplify Command]].}}

Revision as of 09:52, 1 September 2014


TrigCombine

This article is about GeoGebra command.

Command Categories (All commands)


TrigCombine[ <Expression> ]
Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables.
Example: TrigCombine[sin(x) cos(3x)] gives {\frac{1}{2} \; \operatorname{sin} \left( 4 \; x \right) - \frac{1}{2} \; \operatorname{sin} \left( 2 \; x \right)}.
Example: TrigCombine[sin(x) + cos(x)] gives {\sqrt{2} \; \operatorname{cos} \left( x - \frac{1}{4} \; \pi \right)} .
TrigCombine[ <Expression>, <Target Function> ]
Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables, preferring the given target function.
Example: TrigCombine[sin(x) + cos(x), sin(x)] gives {\sqrt{2} \; \operatorname{sin} \left( x + \frac{1}{4} \; \pi \right)} .


CAS Syntax

TrigCombine[ <Expression> ]
Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables.
Example: TrigCombine[sin(p) cos(3p)] gives {\frac{1}{2} \; \operatorname{sin} \left( 4 \; p \right) - \frac{1}{2} \; \operatorname{sin} \left( 2 \; p \right)}.


TrigCombine[ <Expression>, <Target Function> ]
Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables, preferring the given target function.
Example: TrigCombine[sin(p) + cos(p), sin(x)] gives {\sqrt{2} \; \operatorname{sin} \left( p + \frac{1}{4} \; \pi \right)} .


Note: See also TrigExpand Command and TrigSimplify Command.
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