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sin [C++ Reference]
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<h2><a name="sin" id="sin">sin</a></h2>
<div class="level2">
<p>
Syntax:
</p>
<pre class="c code c++" style="font-family:monospace;"> <span class="co2">#include <cmath></span>
<span class="kw4">double</span> sin<span class="br0">(</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy0">;</span></pre>
<p>
The function sin returns the sine of <code>arg</code>, where <code>arg</code> is given in radians. The
return value of sin will be in the range [-1,1]. If <code>arg</code> is infinite, sin
will return NAN and raise a floating-point exception.
</p>
<p>
C++ also provides the following overloaded forms:
</p>
<pre class="c code c++" style="font-family:monospace;"> <span class="co2">#include <cmath></span>
<span class="kw4">float</span> sin<span class="br0">(</span> <span class="kw4">float</span> arg <span class="br0">)</span><span class="sy0">;</span> <span class="co1">// same as sinf() in C99</span>
<span class="kw4">long</span> <span class="kw4">double</span> sin<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy0">;</span> <span class="co1">// same as sinl() in C99</span></pre>
<p>
One possible way to <a href="http://en.wikipedia.org/wiki/Small_angle_approximation" class="urlextern" title="http://en.wikipedia.org/wiki/Small_angle_approximation" rel="nofollow">approximate the sine function using the Taylor series</a> takes advantage of the fact that sin(x) = x - x<sup>3</sup>/3! + x<sup>5</sup>/5! - x<sup>7</sup>/7! + …, yielding the following code:
</p>
<pre class="c code c++" style="font-family:monospace;"><span class="kw4">long</span> factrl<span class="br0">(</span><span class="kw4">int</span> n<span class="br0">)</span> <span class="br0">{</span>
<span class="kw4">long</span> la <span class="sy0">=</span> <span class="nu0">1</span><span class="sy0">;</span>
<span class="kw1">for</span><span class="br0">(</span> <span class="kw4">int</span> i <span class="sy0">=</span> <span class="nu0">2</span><span class="sy0">;</span> i <span class="sy0"><=</span> n<span class="sy0">;</span> i<span class="sy0">++</span> <span class="br0">)</span> la <span class="sy0">*=</span> i<span class="sy0">;</span>
<span class="kw1">return</span> la<span class="sy0">;</span>
<span class="br0">}</span>
<span class="kw4">float</span> sin2<span class="br0">(</span><span class="kw4">float</span> x<span class="br0">)</span> <span class="br0">{</span>
<span class="kw4">int</span> i<span class="sy0">;</span>
<span class="kw4">float</span> y<span class="sy0">=</span>x <span class="sy0">,</span>r<span class="sy0">=</span>x<span class="sy0">;</span>
<span class="kw1">for</span><span class="br0">(</span> <span class="kw4">int</span> i<span class="sy0">=</span><span class="nu0">0</span><span class="sy0">;</span> i <span class="sy0"><</span> <span class="nu0">10</span><span class="sy0">;</span> i<span class="sy0">++</span> <span class="br0">)</span> <span class="br0">{</span>
y <span class="sy0">*=</span> <span class="sy0">-</span>x<span class="sy0">*</span>x<span class="sy0">;</span>
r <span class="sy0">+=</span> 1.0 <span class="sy0">/</span> factrl<span class="br0">(</span> 1<span class="sy0">+</span>2<span class="sy0">*</span><span class="br0">(</span>i<span class="sy0">+</span>1<span class="br0">)</span> <span class="br0">)</span> <span class="sy0">*</span> y<span class="sy0">;</span>
<span class="br0">}</span>
<span class="kw1">return</span> r<span class="sy0">;</span>
<span class="br0">}</span>
<span class="kw4">float</span> sin<span class="br0">(</span><span class="kw4">float</span> theta<span class="br0">)</span> <span class="br0">{</span>
<span class="kw4">float</span> sign <span class="sy0">=</span> 1<span class="sy0">,</span> x <span class="sy0">=</span> theta<span class="sy0">/</span>M_PI<span class="sy0">;</span>
<span class="kw1">if</span> <span class="br0">(</span>x <span class="sy0"><</span> 0.0<span class="br0">)</span> <span class="br0">{</span>
sign <span class="sy0">=</span> <span class="sy0">-</span><span class="nu0">1</span><span class="sy0">;</span>
x <span class="sy0">=</span> <span class="sy0">-</span>x<span class="sy0">;</span>
<span class="br0">}</span>
<span class="kw4">int</span> i <span class="sy0">=</span> static_cast<span class="sy0"><</span>int<span class="sy0">></span><span class="br0">(</span>x<span class="sy0">+</span>0.5<span class="br0">)</span><span class="sy0">;</span>
<span class="kw4">float</span> a <span class="sy0">=</span> x<span class="sy0">-</span>i<span class="sy0">;</span>
<span class="kw1">if</span><span class="br0">(</span> <span class="br0">(</span>i<span class="sy0">-</span>i<span class="sy0">/</span>2<span class="sy0">*</span>2<span class="br0">)</span> <span class="sy0">!=</span> 0 <span class="br0">)</span> sign <span class="sy0">=</span> <span class="sy0">-</span>sign<span class="sy0">;</span>
<span class="kw1">return</span> sign <span class="sy0">*</span> sin2<span class="br0">(</span>a<span class="sy0">*</span>M_PI<span class="br0">)</span><span class="sy0">;</span>
<span class="br0">}</span></pre>
<p>
Related Topics: <a href="../../c/math/acos.html" class="wikilink1" title="c:math:acos">acos</a>, <a href="../../c/math/asin.html" class="wikilink1" title="c:math:asin">asin</a>, <a href="../../c/math/atan.html" class="wikilink1" title="c:math:atan">atan</a>, <a href="../../c/math/atan2.html" class="wikilink1" title="c:math:atan2">atan2</a>, <a href="../../c/math/cos.html" class="wikilink1" title="c:math:cos">cos</a>, <a href="../../c/math/cosh.html" class="wikilink1" title="c:math:cosh">cosh</a>, <a href="../../c/math/sinh.html" class="wikilink1" title="c:math:sinh">sinh</a>, <a href="../../c/math/tan.html" class="wikilink1" title="c:math:tan">tan</a>, <a href="../../c/math/tanh.html" class="wikilink1" title="c:math:tanh">tanh</a>
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