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<p>
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<hr>
<span id="Trigonometry-1"></span><h3 class="section">17.3 Trigonometry</h3>
<p>Octave provides the following trigonometric functions where angles are
specified in radians. To convert from degrees to radians multiply by
<code>pi/180</code>
or use the <code>deg2rad</code> function. For example, <code>sin (30 * pi/180)</code>
returns the sine of 30 degrees. As an alternative, Octave provides a number of
trigonometric functions which work directly on an argument specified in
degrees. These functions are named after the base trigonometric function with
a ‘<samp>d</samp>’ suffix. As an example, <code>sin</code> expects an angle in radians while
<code>sind</code> expects an angle in degrees.
</p>
<p>Octave uses the C library trigonometric functions. It is expected that these
functions are defined by the ISO/IEC 9899 Standard. This Standard is available
at: <a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf">http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf</a>.
Section F.9.1 deals with the trigonometric functions. The behavior of most of
the functions is relatively straightforward. However, there are some
exceptions to the standard behavior. Many of the exceptions involve the
behavior for -0. The most complex case is atan2. Octave exactly implements
the behavior given in the Standard. Including
<code>atan2(+- 0, 0)</code> returns <code>+- pi</code>.
</p>
<p>It should be noted that <small>MATLAB</small> uses different definitions which apparently
do not distinguish -0.
</p>
<span id="XREFdeg2rad"></span><dl class="def">
<dt id="index-deg2rad"><span class="category">: </span><span><em><var>rad</var> =</em> <strong>deg2rad</strong> <em>(<var>deg</var>)</em><a href='#index-deg2rad' class='copiable-anchor'> ¶</a></span></dt>
<dd>
<p>Convert degrees to radians.
</p>
<p>The input <var>deg</var> must be a scalar, vector, or N-dimensional array of
double or single floating point values. <var>deg</var> may be complex in which
case the real and imaginary components are converted separately.
</p>
<p>The output <var>rad</var> is the same size and shape as <var>deg</var> with degrees
converted to radians using the conversion constant <code>pi/180</code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">deg2rad ([0, 90, 180, 270, 360])
⇒ 0.00000 1.57080 3.14159 4.71239 6.28319
</pre></div>
<p><strong>See also:</strong> <a href="#XREFrad2deg">rad2deg</a>.
</p></dd></dl>
<span id="XREFrad2deg"></span><dl class="def">
<dt id="index-rad2deg"><span class="category">: </span><span><em><var>deg</var> =</em> <strong>rad2deg</strong> <em>(<var>rad</var>)</em><a href='#index-rad2deg' class='copiable-anchor'> ¶</a></span></dt>
<dd>
<p>Convert radians to degrees.
</p>
<p>The input <var>rad</var> must be a scalar, vector, or N-dimensional array of
double or single floating point values. <var>rad</var> may be complex in which
case the real and imaginary components are converted separately.
</p>
<p>The output <var>deg</var> is the same size and shape as <var>rad</var> with radians
converted to degrees using the conversion constant <code>180/pi</code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">rad2deg ([0, pi/2, pi, 3/2*pi, 2*pi])
⇒ 0 90 180 270 360
</pre></div>
<p><strong>See also:</strong> <a href="#XREFdeg2rad">deg2rad</a>.
</p></dd></dl>
<span id="XREFsin"></span><dl class="def">
<dt id="index-sin"><span class="category">: </span><span><em></em> <strong>sin</strong> <em>(<var>x</var>)</em><a href='#index-sin' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the sine for each element of <var>x</var> in radians.
</p>
<p><strong>See also:</strong> <a href="#XREFasin">asin</a>, <a href="#XREFsind">sind</a>, <a href="#XREFsinh">sinh</a>.
</p></dd></dl>
<span id="XREFcos"></span><dl class="def">
<dt id="index-cos"><span class="category">: </span><span><em></em> <strong>cos</strong> <em>(<var>x</var>)</em><a href='#index-cos' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the cosine for each element of <var>x</var> in radians.
</p>
<p><strong>See also:</strong> <a href="#XREFacos">acos</a>, <a href="#XREFcosd">cosd</a>, <a href="#XREFcosh">cosh</a>.
</p></dd></dl>
<span id="XREFtan"></span><dl class="def">
<dt id="index-tan"><span class="category">: </span><span><em></em> <strong>tan</strong> <em>(<var>z</var>)</em><a href='#index-tan' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the tangent for each element of <var>x</var> in radians.
</p>
<p><strong>See also:</strong> <a href="#XREFatan">atan</a>, <a href="#XREFtand">tand</a>, <a href="#XREFtanh">tanh</a>.
</p></dd></dl>
<span id="XREFsec"></span><dl class="def">
<dt id="index-sec"><span class="category">: </span><span><em></em> <strong>sec</strong> <em>(<var>x</var>)</em><a href='#index-sec' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the secant for each element of <var>x</var> in radians.
</p>
<p><strong>See also:</strong> <a href="#XREFasec">asec</a>, <a href="#XREFsecd">secd</a>, <a href="#XREFsech">sech</a>.
</p></dd></dl>
<span id="XREFcsc"></span><dl class="def">
<dt id="index-csc"><span class="category">: </span><span><em></em> <strong>csc</strong> <em>(<var>x</var>)</em><a href='#index-csc' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the cosecant for each element of <var>x</var> in radians.
</p>
<p><strong>See also:</strong> <a href="#XREFacsc">acsc</a>, <a href="#XREFcscd">cscd</a>, <a href="#XREFcsch">csch</a>.
</p></dd></dl>
<span id="XREFcot"></span><dl class="def">
<dt id="index-cot"><span class="category">: </span><span><em></em> <strong>cot</strong> <em>(<var>x</var>)</em><a href='#index-cot' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the cotangent for each element of <var>x</var> in radians.
</p>
<p><strong>See also:</strong> <a href="#XREFacot">acot</a>, <a href="#XREFcotd">cotd</a>, <a href="#XREFcoth">coth</a>.
</p></dd></dl>
<span id="XREFasin"></span><dl class="def">
<dt id="index-asin"><span class="category">: </span><span><em></em> <strong>asin</strong> <em>(<var>x</var>)</em><a href='#index-asin' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse sine in radians for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFsin">sin</a>, <a href="#XREFasind">asind</a>.
</p></dd></dl>
<span id="XREFacos"></span><dl class="def">
<dt id="index-acos"><span class="category">: </span><span><em></em> <strong>acos</strong> <em>(<var>x</var>)</em><a href='#index-acos' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse cosine in radians for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcos">cos</a>, <a href="#XREFacosd">acosd</a>.
</p></dd></dl>
<span id="XREFatan"></span><dl class="def">
<dt id="index-atan"><span class="category">: </span><span><em></em> <strong>atan</strong> <em>(<var>x</var>)</em><a href='#index-atan' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse tangent in radians for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFtan">tan</a>, <a href="#XREFatand">atand</a>.
</p></dd></dl>
<span id="XREFasec"></span><dl class="def">
<dt id="index-asec"><span class="category">: </span><span><em></em> <strong>asec</strong> <em>(<var>x</var>)</em><a href='#index-asec' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse secant in radians for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFsec">sec</a>, <a href="#XREFasecd">asecd</a>.
</p></dd></dl>
<span id="XREFacsc"></span><dl class="def">
<dt id="index-acsc"><span class="category">: </span><span><em></em> <strong>acsc</strong> <em>(<var>x</var>)</em><a href='#index-acsc' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse cosecant in radians for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcsc">csc</a>, <a href="#XREFacscd">acscd</a>.
</p></dd></dl>
<span id="XREFacot"></span><dl class="def">
<dt id="index-acot"><span class="category">: </span><span><em></em> <strong>acot</strong> <em>(<var>x</var>)</em><a href='#index-acot' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse cotangent in radians for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcot">cot</a>, <a href="#XREFacotd">acotd</a>.
</p></dd></dl>
<span id="XREFsinh"></span><dl class="def">
<dt id="index-sinh"><span class="category">: </span><span><em></em> <strong>sinh</strong> <em>(<var>x</var>)</em><a href='#index-sinh' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the hyperbolic sine for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFasinh">asinh</a>, <a href="#XREFcosh">cosh</a>, <a href="#XREFtanh">tanh</a>.
</p></dd></dl>
<span id="XREFcosh"></span><dl class="def">
<dt id="index-cosh"><span class="category">: </span><span><em></em> <strong>cosh</strong> <em>(<var>x</var>)</em><a href='#index-cosh' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the hyperbolic cosine for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFacosh">acosh</a>, <a href="#XREFsinh">sinh</a>, <a href="#XREFtanh">tanh</a>.
</p></dd></dl>
<span id="XREFtanh"></span><dl class="def">
<dt id="index-tanh"><span class="category">: </span><span><em></em> <strong>tanh</strong> <em>(<var>x</var>)</em><a href='#index-tanh' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute hyperbolic tangent for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFatanh">atanh</a>, <a href="#XREFsinh">sinh</a>, <a href="#XREFcosh">cosh</a>.
</p></dd></dl>
<span id="XREFsech"></span><dl class="def">
<dt id="index-sech"><span class="category">: </span><span><em></em> <strong>sech</strong> <em>(<var>x</var>)</em><a href='#index-sech' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the hyperbolic secant of each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFasech">asech</a>.
</p></dd></dl>
<span id="XREFcsch"></span><dl class="def">
<dt id="index-csch"><span class="category">: </span><span><em></em> <strong>csch</strong> <em>(<var>x</var>)</em><a href='#index-csch' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the hyperbolic cosecant of each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFacsch">acsch</a>.
</p></dd></dl>
<span id="XREFcoth"></span><dl class="def">
<dt id="index-coth"><span class="category">: </span><span><em></em> <strong>coth</strong> <em>(<var>x</var>)</em><a href='#index-coth' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the hyperbolic cotangent of each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFacoth">acoth</a>.
</p></dd></dl>
<span id="XREFasinh"></span><dl class="def">
<dt id="index-asinh"><span class="category">: </span><span><em></em> <strong>asinh</strong> <em>(<var>x</var>)</em><a href='#index-asinh' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse hyperbolic sine for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFsinh">sinh</a>.
</p></dd></dl>
<span id="XREFacosh"></span><dl class="def">
<dt id="index-acosh"><span class="category">: </span><span><em></em> <strong>acosh</strong> <em>(<var>x</var>)</em><a href='#index-acosh' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse hyperbolic cosine for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcosh">cosh</a>.
</p></dd></dl>
<span id="XREFatanh"></span><dl class="def">
<dt id="index-atanh"><span class="category">: </span><span><em></em> <strong>atanh</strong> <em>(<var>x</var>)</em><a href='#index-atanh' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse hyperbolic tangent for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFtanh">tanh</a>.
</p></dd></dl>
<span id="XREFasech"></span><dl class="def">
<dt id="index-asech"><span class="category">: </span><span><em></em> <strong>asech</strong> <em>(<var>x</var>)</em><a href='#index-asech' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse hyperbolic secant of each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFsech">sech</a>.
</p></dd></dl>
<span id="XREFacsch"></span><dl class="def">
<dt id="index-acsch"><span class="category">: </span><span><em></em> <strong>acsch</strong> <em>(<var>x</var>)</em><a href='#index-acsch' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse hyperbolic cosecant of each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcsch">csch</a>.
</p></dd></dl>
<span id="XREFacoth"></span><dl class="def">
<dt id="index-acoth"><span class="category">: </span><span><em></em> <strong>acoth</strong> <em>(<var>x</var>)</em><a href='#index-acoth' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse hyperbolic cotangent of each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcoth">coth</a>.
</p></dd></dl>
<span id="XREFatan2"></span><dl class="def">
<dt id="index-atan2"><span class="category">: </span><span><em></em> <strong>atan2</strong> <em>(<var>y</var>, <var>x</var>)</em><a href='#index-atan2' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute atan (<var>y</var> / <var>x</var>) for corresponding elements of <var>y</var>
and <var>x</var>.
</p>
<p><var>y</var> and <var>x</var> must match in size and orientation. The signs of
elements of <var>y</var> and <var>x</var> are used to determine the quadrants of each
resulting value.
</p>
<p>This function is equivalent to <code>arg (complex (<var>x</var>, <var>y</var>))</code>.
</p>
<p><strong>See also:</strong> <a href="#XREFtan">tan</a>, <a href="#XREFtand">tand</a>, <a href="#XREFtanh">tanh</a>, <a href="#XREFatanh">atanh</a>.
</p></dd></dl>
<p>Octave provides the following trigonometric functions where angles are
specified in degrees. These functions produce true zeros at the appropriate
intervals rather than the small round-off error that occurs when using
radians. For example:
</p>
<div class="example">
<pre class="example">cosd (90)
⇒ 0
cos (pi/2)
⇒ 6.1230e-17
</pre></div>
<span id="XREFsind"></span><dl class="def">
<dt id="index-sind"><span class="category">: </span><span><em></em> <strong>sind</strong> <em>(<var>x</var>)</em><a href='#index-sind' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the sine for each element of <var>x</var> in degrees.
</p>
<p>The function is more accurate than <code>sin</code> for large values of <var>x</var>
and for multiples of 180 degrees (<code><var>x</var>/180</code> is an integer) where
<code>sind</code> returns 0 rather than a small value on the order of eps.
</p>
<p><strong>See also:</strong> <a href="#XREFasind">asind</a>, <a href="#XREFsin">sin</a>.
</p></dd></dl>
<span id="XREFcosd"></span><dl class="def">
<dt id="index-cosd"><span class="category">: </span><span><em></em> <strong>cosd</strong> <em>(<var>x</var>)</em><a href='#index-cosd' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the cosine for each element of <var>x</var> in degrees.
</p>
<p>The function is more accurate than <code>cos</code> for large values of <var>x</var>
and for multiples of 90 degrees (<code><var>x</var> = 90 + 180*n</code> with n an
integer) where <code>cosd</code> returns 0 rather than a small value on the order
of eps.
</p>
<p><strong>See also:</strong> <a href="#XREFacosd">acosd</a>, <a href="#XREFcos">cos</a>.
</p></dd></dl>
<span id="XREFtand"></span><dl class="def">
<dt id="index-tand"><span class="category">: </span><span><em></em> <strong>tand</strong> <em>(<var>x</var>)</em><a href='#index-tand' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the tangent for each element of <var>x</var> in degrees.
</p>
<p>Returns zero for elements where <code><var>x</var>/180</code> is an integer and
<code>Inf</code> for elements where <code>(<var>x</var>-90)/180</code> is an integer.
</p>
<p><strong>See also:</strong> <a href="#XREFatand">atand</a>, <a href="#XREFtan">tan</a>.
</p></dd></dl>
<span id="XREFsecd"></span><dl class="def">
<dt id="index-secd"><span class="category">: </span><span><em></em> <strong>secd</strong> <em>(<var>x</var>)</em><a href='#index-secd' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the secant for each element of <var>x</var> in degrees.
</p>
<p><strong>See also:</strong> <a href="#XREFasecd">asecd</a>, <a href="#XREFsec">sec</a>.
</p></dd></dl>
<span id="XREFcscd"></span><dl class="def">
<dt id="index-cscd"><span class="category">: </span><span><em></em> <strong>cscd</strong> <em>(<var>x</var>)</em><a href='#index-cscd' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the cosecant for each element of <var>x</var> in degrees.
</p>
<p><strong>See also:</strong> <a href="#XREFacscd">acscd</a>, <a href="#XREFcsc">csc</a>.
</p></dd></dl>
<span id="XREFcotd"></span><dl class="def">
<dt id="index-cotd"><span class="category">: </span><span><em></em> <strong>cotd</strong> <em>(<var>x</var>)</em><a href='#index-cotd' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the cotangent for each element of <var>x</var> in degrees.
</p>
<p><strong>See also:</strong> <a href="#XREFacotd">acotd</a>, <a href="#XREFcot">cot</a>.
</p></dd></dl>
<span id="XREFasind"></span><dl class="def">
<dt id="index-asind"><span class="category">: </span><span><em></em> <strong>asind</strong> <em>(<var>x</var>)</em><a href='#index-asind' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse sine in degrees for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFsind">sind</a>, <a href="#XREFasin">asin</a>.
</p></dd></dl>
<span id="XREFacosd"></span><dl class="def">
<dt id="index-acosd"><span class="category">: </span><span><em></em> <strong>acosd</strong> <em>(<var>x</var>)</em><a href='#index-acosd' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse cosine in degrees for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcosd">cosd</a>, <a href="#XREFacos">acos</a>.
</p></dd></dl>
<span id="XREFatand"></span><dl class="def">
<dt id="index-atand"><span class="category">: </span><span><em></em> <strong>atand</strong> <em>(<var>x</var>)</em><a href='#index-atand' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse tangent in degrees for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFtand">tand</a>, <a href="#XREFatan">atan</a>.
</p></dd></dl>
<span id="XREFatan2d"></span><dl class="def">
<dt id="index-atan2d"><span class="category">: </span><span><em></em> <strong>atan2d</strong> <em>(<var>y</var>, <var>x</var>)</em><a href='#index-atan2d' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute atan (<var>y</var> / <var>x</var>) in degrees for corresponding elements
from <var>y</var> and <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFtand">tand</a>, <a href="#XREFatan2">atan2</a>.
</p></dd></dl>
<span id="XREFasecd"></span><dl class="def">
<dt id="index-asecd"><span class="category">: </span><span><em></em> <strong>asecd</strong> <em>(<var>x</var>)</em><a href='#index-asecd' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse secant in degrees for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFsecd">secd</a>, <a href="#XREFasec">asec</a>.
</p></dd></dl>
<span id="XREFacscd"></span><dl class="def">
<dt id="index-acscd"><span class="category">: </span><span><em></em> <strong>acscd</strong> <em>(<var>x</var>)</em><a href='#index-acscd' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse cosecant in degrees for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcscd">cscd</a>, <a href="#XREFacsc">acsc</a>.
</p></dd></dl>
<span id="XREFacotd"></span><dl class="def">
<dt id="index-acotd"><span class="category">: </span><span><em></em> <strong>acotd</strong> <em>(<var>x</var>)</em><a href='#index-acotd' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute the inverse cotangent in degrees for each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFcotd">cotd</a>, <a href="#XREFacot">acot</a>.
</p></dd></dl>
<p>Finally, there are two trigonometric functions that calculate special
arguments with increased accuracy.
</p>
<span id="XREFsinpi"></span><dl class="def">
<dt id="index-sinpi"><span class="category">: </span><span><em><var>y</var> =</em> <strong>sinpi</strong> <em>(<var>x</var>)</em><a href='#index-sinpi' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute sine (<var>x</var> * pi) for each element of <var>x</var> accurately.
</p>
<p>The ordinary <code>sin</code> function uses IEEE floating point numbers and may
produce results that are very close (within a few eps) of the correct
value, but which are not exact. The <code>sinpi</code> function is more accurate
and returns 0 exactly for integer values of <var>x</var> and +1/-1 for
half-integer values (e.g., …, -3/2, -1/2, 1/2, 3/2, …).
</p>
<p>Example <br>
comparison of <code>sin</code> and <code>sinpi</code> for integer values of <var>x</var>
</p>
<div class="example">
<pre class="example">sin ([0, 1, 2, 3] * pi)
⇒
0 1.2246e-16 -2.4493e-16 3.6739e-16
sinpi ([0, 1, 2, 3])
⇒
0 0 0 0
</pre></div>
<p><strong>See also:</strong> <a href="#XREFcospi">cospi</a>, <a href="#XREFsin">sin</a>.
</p></dd></dl>
<span id="XREFcospi"></span><dl class="def">
<dt id="index-cospi"><span class="category">: </span><span><em><var>y</var> =</em> <strong>cospi</strong> <em>(<var>x</var>)</em><a href='#index-cospi' class='copiable-anchor'> ¶</a></span></dt>
<dd><p>Compute cosine (<var>x</var> * pi) for each element of <var>x</var> accurately.
</p>
<p>The ordinary <code>cos</code> function uses IEEE floating point numbers and may
produce results that are very close (within a few eps) of the correct
value, but which are not exact. The <code>cospi</code> function is more accurate
and returns 0 exactly for half-integer values of <var>x</var> (e.g., …,
-3/2, -1/2, 1/2, 3/2, …), and +1/-1 for integer values.
</p>
<p>Example <br>
comparison of <code>cos</code> and <code>cospi</code> for half-integer values of <var>x</var>
</p>
<div class="example">
<pre class="example">cos ([-3/2, -1/2, 1/2, 3/2] * pi)
⇒
-1.8370e-16 6.1232e-17 6.1232e-17 -1.8370e-16
cospi ([-3/2, -1/2, 1/2, 3/2])
⇒
0 0 0 0
</pre></div>
<p><strong>See also:</strong> <a href="#XREFsinpi">sinpi</a>, <a href="#XREFcos">cos</a>.
</p></dd></dl>
</div>
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