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<a name="Factor-Sums-of-sin-and-cos-Functions"></a>
<div class="header">
<p>
Next: <a href="maxima_398.html#Solve-Trignometric-Equations" accesskey="n" rel="next">Solve Trignometric Equations</a>, Previous: <a href="maxima_396.html#Convert-to-Hyperbolic-Functions" accesskey="p" rel="previous">Convert to Hyperbolic Functions</a>, Up: <a href="maxima_393.html#Functions-and-Variables-for-trigtools" accesskey="u" rel="up">Functions and Variables for trigtools</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Factor-Sums-of-sin-and-cos-Functions-1"></a>
<h4 class="subsection">96.2.4 Factor Sums of sin and cos Functions</h4>
<a name="trigfactor"></a><a name="Item_003a-trigtools_002fdeffn_002ftrigfactor"></a><dl>
<dt><a name="index-trigfactor"></a>Function: <strong>trigfactor</strong> <em>(<var>x</var>)</em></dt>
<dd><p>The function trigfactor factors expresions of
form
\(\pm \sin x \pm \cos y.\)</p>
<p>Examples:
</p>
<ol>
<li> <!-- /@w -->
<div class="example">
<pre class="example">(%i2) trigfactor(sin(x)+cos(x));
%pi
(%o2) sqrt(2) cos(x - ---)
4
(%i3) trigrat(%);
(%o3) sin(x) + cos(x)
</pre></div>
</li><li> <!-- /@w -->
<div class="example">
<pre class="example">(%i4) trigfactor(sin(x)+cos(y));
y x %pi y x %pi
(%o4) 2 cos(- - - + ---) cos(- + - - ---)
2 2 4 2 2 4
</pre><pre class="example">(%i5) trigrat(%);
(%o5) cos(y) + sin(x)
</pre></div>
</li><li> <!-- /@w -->
<div class="example">
<pre class="example">(%i6) trigfactor(sin(x)-cos(3*y));
3 y x %pi 3 y x %pi
(%o6) 2 sin(--- - - + ---) sin(--- + - - ---)
2 2 4 2 2 4
(%i7) trigrat(%);
(%o7) sin(x) - cos(3 y)
</pre></div>
</li><li> <!-- /@w -->
<div class="example">
<pre class="example">(%i8) trigfactor(-sin(5*x)-cos(3*y));
3 y 5 x %pi 3 y 5 x %pi
(%o8) - 2 cos(--- - --- + ---) cos(--- + --- - ---)
2 2 4 2 2 4
(%i9) trigrat(%);
(%o9) (- cos(3 y)) - sin(5 x)
</pre></div>
</li><li> <!-- /@w -->
<div class="example">
<pre class="example">(%i10) sin(alpha)+sin(beta)=trigfactor(sin(alpha)+sin(beta));
beta alpha beta alpha
(%o10) sin(beta) + sin(alpha) = 2 cos(---- - -----) sin(---- + -----)
2 2 2 2
</pre><pre class="example">(%i11) trigrat(%);
(%o78) sin(beta) + sin(alpha) = sin(beta) + sin(alpha)
</pre></div>
</li><li> <!-- /@w -->
<div class="example">
<pre class="example">(%i12) sin(alpha)-sin(beta)=trigfactor(sin(alpha)-sin(beta));
beta alpha beta alpha
(%o12) sin(alpha) - sin(beta) = - 2 sin(---- - -----) cos(---- + -----)
2 2 2 2
</pre></div>
</li><li> <!-- /@w -->
<div class="example">
<pre class="example">(%i13) cos(alpha)+cos(beta)=trigfactor(cos(alpha)+cos(beta));
beta alpha beta alpha
(%o80) cos(beta) + cos(alpha) = 2 cos(---- - -----) cos(---- + -----)
2 2 2 2
</pre></div>
</li><li> <!-- /@w -->
<div class="example">
<pre class="example">(%i14) cos(alpha)-cos(beta)=trigfactor(cos(alpha)-cos(beta));
beta alpha beta alpha
(%o14) cos(alpha) - cos(beta) = 2 sin(---- - -----) sin(---- + -----)
2 2 2 2
</pre></div>
</li><li> <!-- /@w -->
<div class="example">
<pre class="example">(%i15) trigfactor(3*sin(x)+7*cos(x));
(%o15) 3 sin(x) + 7 cos(x)
</pre><pre class="example">(%i16) c2sin(%);
7
(%o16) sqrt(58) sin(x + atan(-))
3
</pre><pre class="example">(%i17) trigexpand(%),expand;
(%o17) 3 sin(x) + 7 cos(x)
</pre></div>
<p>10.
</p><div class="example">
<pre class="example">(%i18) trigfactor(sin(2*x));
(%o18) sin(2 x)
(%i19) trigexpand(%);
(%o19) 2 cos(x) sin(x)
</pre></div>
</li></ol>
</dd></dl>
<a name="Item_003a-trigtools_002fnode_002fSolve-Trignometric-Equations"></a><hr>
<div class="header">
<p>
Next: <a href="maxima_398.html#Solve-Trignometric-Equations" accesskey="n" rel="next">Solve Trignometric Equations</a>, Previous: <a href="maxima_396.html#Convert-to-Hyperbolic-Functions" accesskey="p" rel="previous">Convert to Hyperbolic Functions</a>, Up: <a href="maxima_393.html#Functions-and-Variables-for-trigtools" accesskey="u" rel="up">Functions and Variables for trigtools</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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