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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>9.3. Mathematical Functions and Operators</title><link rel="stylesheet" type="text/css" href="stylesheet.css" /><link rev="made" href="pgsql-docs@lists.postgresql.org" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="prev" href="functions-comparison.html" title="9.2. Comparison Functions and Operators" /><link rel="next" href="functions-string.html" title="9.4. String Functions and Operators" /></head><body><div xmlns="http://www.w3.org/TR/xhtml1/transitional" class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="5" align="center">9.3. Mathematical Functions and Operators</th></tr><tr><td width="10%" align="left"><a accesskey="p" href="functions-comparison.html" title="9.2. Comparison Functions and Operators">Prev</a> </td><td width="10%" align="left"><a accesskey="u" href="functions.html" title="Chapter 9. Functions and Operators">Up</a></td><th width="60%" align="center">Chapter 9. Functions and Operators</th><td width="10%" align="right"><a accesskey="h" href="index.html" title="PostgreSQL 11.5 Documentation">Home</a></td><td width="10%" align="right"> <a accesskey="n" href="functions-string.html" title="9.4. String Functions and Operators">Next</a></td></tr></table><hr></hr></div><div class="sect1" id="FUNCTIONS-MATH"><div class="titlepage"><div><div><h2 class="title" style="clear: both">9.3. Mathematical Functions and Operators</h2></div></div></div><p>
Mathematical operators are provided for many
<span class="productname">PostgreSQL</span> types. For types without
standard mathematical conventions
(e.g., date/time types) we
describe the actual behavior in subsequent sections.
</p><p>
<a class="xref" href="functions-math.html#FUNCTIONS-MATH-OP-TABLE" title="Table 9.4. Mathematical Operators">Table 9.4</a> shows the available mathematical operators.
</p><div class="table" id="FUNCTIONS-MATH-OP-TABLE"><p class="title"><strong>Table 9.4. Mathematical Operators</strong></p><div class="table-contents"><table class="table" summary="Mathematical Operators" border="1"><colgroup><col /><col /><col /><col /></colgroup><thead><tr><th>Operator</th><th>Description</th><th>Example</th><th>Result</th></tr></thead><tbody><tr><td> <code class="literal">+</code> </td><td>addition</td><td><code class="literal">2 + 3</code></td><td><code class="literal">5</code></td></tr><tr><td> <code class="literal">-</code> </td><td>subtraction</td><td><code class="literal">2 - 3</code></td><td><code class="literal">-1</code></td></tr><tr><td> <code class="literal">*</code> </td><td>multiplication</td><td><code class="literal">2 * 3</code></td><td><code class="literal">6</code></td></tr><tr><td> <code class="literal">/</code> </td><td>division (integer division truncates the result)</td><td><code class="literal">4 / 2</code></td><td><code class="literal">2</code></td></tr><tr><td> <code class="literal">%</code> </td><td>modulo (remainder)</td><td><code class="literal">5 % 4</code></td><td><code class="literal">1</code></td></tr><tr><td> <code class="literal">^</code> </td><td>exponentiation (associates left to right)</td><td><code class="literal">2.0 ^ 3.0</code></td><td><code class="literal">8</code></td></tr><tr><td> <code class="literal">|/</code> </td><td>square root</td><td><code class="literal">|/ 25.0</code></td><td><code class="literal">5</code></td></tr><tr><td> <code class="literal">||/</code> </td><td>cube root</td><td><code class="literal">||/ 27.0</code></td><td><code class="literal">3</code></td></tr><tr><td> <code class="literal">!</code> </td><td>factorial</td><td><code class="literal">5 !</code></td><td><code class="literal">120</code></td></tr><tr><td> <code class="literal">!!</code> </td><td>factorial (prefix operator)</td><td><code class="literal">!! 5</code></td><td><code class="literal">120</code></td></tr><tr><td> <code class="literal">@</code> </td><td>absolute value</td><td><code class="literal">@ -5.0</code></td><td><code class="literal">5</code></td></tr><tr><td> <code class="literal">&</code> </td><td>bitwise AND</td><td><code class="literal">91 & 15</code></td><td><code class="literal">11</code></td></tr><tr><td> <code class="literal">|</code> </td><td>bitwise OR</td><td><code class="literal">32 | 3</code></td><td><code class="literal">35</code></td></tr><tr><td> <code class="literal">#</code> </td><td>bitwise XOR</td><td><code class="literal">17 # 5</code></td><td><code class="literal">20</code></td></tr><tr><td> <code class="literal">~</code> </td><td>bitwise NOT</td><td><code class="literal">~1</code></td><td><code class="literal">-2</code></td></tr><tr><td> <code class="literal"><<</code> </td><td>bitwise shift left</td><td><code class="literal">1 << 4</code></td><td><code class="literal">16</code></td></tr><tr><td> <code class="literal">>></code> </td><td>bitwise shift right</td><td><code class="literal">8 >> 2</code></td><td><code class="literal">2</code></td></tr></tbody></table></div></div><br class="table-break" /><p>
The bitwise operators work only on integral data types, whereas
the others are available for all numeric data types. The bitwise
operators are also available for the bit
string types <code class="type">bit</code> and <code class="type">bit varying</code>, as
shown in <a class="xref" href="functions-bitstring.html#FUNCTIONS-BIT-STRING-OP-TABLE" title="Table 9.13. Bit String Operators">Table 9.13</a>.
</p><p>
<a class="xref" href="functions-math.html#FUNCTIONS-MATH-FUNC-TABLE" title="Table 9.5. Mathematical Functions">Table 9.5</a> shows the available
mathematical functions. In the table, <code class="literal">dp</code>
indicates <code class="type">double precision</code>. Many of these functions
are provided in multiple forms with different argument types.
Except where noted, any given form of a function returns the same
data type as its argument.
The functions working with <code class="type">double precision</code> data are mostly
implemented on top of the host system's C library; accuracy and behavior in
boundary cases can therefore vary depending on the host system.
</p><div class="table" id="FUNCTIONS-MATH-FUNC-TABLE"><p class="title"><strong>Table 9.5. Mathematical Functions</strong></p><div class="table-contents"><table class="table" summary="Mathematical Functions" border="1"><colgroup><col /><col /><col /><col /><col /></colgroup><thead><tr><th>Function</th><th>Return Type</th><th>Description</th><th>Example</th><th>Result</th></tr></thead><tbody><tr><td>
<a id="id-1.5.8.8.7.2.2.1.1.1" class="indexterm"></a>
<code class="literal"><code class="function">abs(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>(same as input)</td><td>absolute value</td><td><code class="literal">abs(-17.4)</code></td><td><code class="literal">17.4</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.2.1.1" class="indexterm"></a>
<code class="literal"><code class="function">cbrt(<code class="type">dp</code>)</code></code>
</td><td><code class="type">dp</code></td><td>cube root</td><td><code class="literal">cbrt(27.0)</code></td><td><code class="literal">3</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.3.1.1" class="indexterm"></a>
<code class="literal"><code class="function">ceil(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>nearest integer greater than or equal to argument</td><td><code class="literal">ceil(-42.8)</code></td><td><code class="literal">-42</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.4.1.1" class="indexterm"></a>
<code class="literal"><code class="function">ceiling(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>nearest integer greater than or equal to argument (same as <code class="function">ceil</code>)</td><td><code class="literal">ceiling(-95.3)</code></td><td><code class="literal">-95</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.5.1.1" class="indexterm"></a>
<code class="literal"><code class="function">degrees(<code class="type">dp</code>)</code></code>
</td><td><code class="type">dp</code></td><td>radians to degrees</td><td><code class="literal">degrees(0.5)</code></td><td><code class="literal">28.6478897565412</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.6.1.1" class="indexterm"></a>
<code class="literal"><code class="function">div(<em class="parameter"><code>y</code></em> <code class="type">numeric</code>,
<em class="parameter"><code>x</code></em> <code class="type">numeric</code>)</code></code>
</td><td><code class="type">numeric</code></td><td>integer quotient of <em class="parameter"><code>y</code></em>/<em class="parameter"><code>x</code></em></td><td><code class="literal">div(9,4)</code></td><td><code class="literal">2</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.7.1.1" class="indexterm"></a>
<code class="literal"><code class="function">exp(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>exponential</td><td><code class="literal">exp(1.0)</code></td><td><code class="literal">2.71828182845905</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.8.1.1" class="indexterm"></a>
<code class="literal"><code class="function">floor(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>nearest integer less than or equal to argument</td><td><code class="literal">floor(-42.8)</code></td><td><code class="literal">-43</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.9.1.1" class="indexterm"></a>
<code class="literal"><code class="function">ln(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>natural logarithm</td><td><code class="literal">ln(2.0)</code></td><td><code class="literal">0.693147180559945</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.10.1.1" class="indexterm"></a>
<code class="literal"><code class="function">log(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>base 10 logarithm</td><td><code class="literal">log(100.0)</code></td><td><code class="literal">2</code></td></tr><tr><td><code class="literal"><code class="function">log(<em class="parameter"><code>b</code></em> <code class="type">numeric</code>,
<em class="parameter"><code>x</code></em> <code class="type">numeric</code>)</code></code></td><td><code class="type">numeric</code></td><td>logarithm to base <em class="parameter"><code>b</code></em></td><td><code class="literal">log(2.0, 64.0)</code></td><td><code class="literal">6.0000000000</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.12.1.1" class="indexterm"></a>
<code class="literal"><code class="function">mod(<em class="parameter"><code>y</code></em>,
<em class="parameter"><code>x</code></em>)</code></code>
</td><td>(same as argument types)</td><td>remainder of <em class="parameter"><code>y</code></em>/<em class="parameter"><code>x</code></em></td><td><code class="literal">mod(9,4)</code></td><td><code class="literal">1</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.13.1.1" class="indexterm"></a>
<code class="literal"><code class="function">pi()</code></code>
</td><td><code class="type">dp</code></td><td><span class="quote">“<span class="quote">π</span>”</span> constant</td><td><code class="literal">pi()</code></td><td><code class="literal">3.14159265358979</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.14.1.1" class="indexterm"></a>
<code class="literal"><code class="function">power(<em class="parameter"><code>a</code></em> <code class="type">dp</code>,
<em class="parameter"><code>b</code></em> <code class="type">dp</code>)</code></code>
</td><td><code class="type">dp</code></td><td><em class="parameter"><code>a</code></em> raised to the power of <em class="parameter"><code>b</code></em></td><td><code class="literal">power(9.0, 3.0)</code></td><td><code class="literal">729</code></td></tr><tr><td><code class="literal"><code class="function">power(<em class="parameter"><code>a</code></em> <code class="type">numeric</code>,
<em class="parameter"><code>b</code></em> <code class="type">numeric</code>)</code></code></td><td><code class="type">numeric</code></td><td><em class="parameter"><code>a</code></em> raised to the power of <em class="parameter"><code>b</code></em></td><td><code class="literal">power(9.0, 3.0)</code></td><td><code class="literal">729</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.16.1.1" class="indexterm"></a>
<code class="literal"><code class="function">radians(<code class="type">dp</code>)</code></code>
</td><td><code class="type">dp</code></td><td>degrees to radians</td><td><code class="literal">radians(45.0)</code></td><td><code class="literal">0.785398163397448</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.17.1.1" class="indexterm"></a>
<code class="literal"><code class="function">round(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>round to nearest integer</td><td><code class="literal">round(42.4)</code></td><td><code class="literal">42</code></td></tr><tr><td><code class="literal"><code class="function">round(<em class="parameter"><code>v</code></em> <code class="type">numeric</code>, <em class="parameter"><code>s</code></em> <code class="type">int</code>)</code></code></td><td><code class="type">numeric</code></td><td>round to <em class="parameter"><code>s</code></em> decimal places</td><td><code class="literal">round(42.4382, 2)</code></td><td><code class="literal">42.44</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.19.1.1" class="indexterm"></a>
<code class="literal"><code class="function">scale(<code class="type">numeric</code>)</code></code>
</td><td><code class="type">integer</code></td><td>scale of the argument (the number of decimal digits in the fractional part)</td><td><code class="literal">scale(8.41)</code></td><td><code class="literal">2</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.20.1.1" class="indexterm"></a>
<code class="literal"><code class="function">sign(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>sign of the argument (-1, 0, +1)</td><td><code class="literal">sign(-8.4)</code></td><td><code class="literal">-1</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.21.1.1" class="indexterm"></a>
<code class="literal"><code class="function">sqrt(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>square root</td><td><code class="literal">sqrt(2.0)</code></td><td><code class="literal">1.4142135623731</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.22.1.1" class="indexterm"></a>
<code class="literal"><code class="function">trunc(<code class="type">dp</code> or <code class="type">numeric</code>)</code></code>
</td><td>(same as input)</td><td>truncate toward zero</td><td><code class="literal">trunc(42.8)</code></td><td><code class="literal">42</code></td></tr><tr><td><code class="literal"><code class="function">trunc(<em class="parameter"><code>v</code></em> <code class="type">numeric</code>, <em class="parameter"><code>s</code></em> <code class="type">int</code>)</code></code></td><td><code class="type">numeric</code></td><td>truncate to <em class="parameter"><code>s</code></em> decimal places</td><td><code class="literal">trunc(42.4382, 2)</code></td><td><code class="literal">42.43</code></td></tr><tr><td>
<a id="id-1.5.8.8.7.2.2.24.1.1" class="indexterm"></a>
<code class="literal"><code class="function">width_bucket(<em class="parameter"><code>operand</code></em> <code class="type">dp</code>, <em class="parameter"><code>b1</code></em> <code class="type">dp</code>, <em class="parameter"><code>b2</code></em> <code class="type">dp</code>, <em class="parameter"><code>count</code></em> <code class="type">int</code>)</code></code></td><td><code class="type">int</code></td><td>return the bucket number to which <em class="parameter"><code>operand</code></em> would
be assigned in a histogram having <em class="parameter"><code>count</code></em> equal-width
buckets spanning the range <em class="parameter"><code>b1</code></em> to <em class="parameter"><code>b2</code></em>;
returns <code class="literal">0</code> or <code class="literal"><em class="parameter"><code>count</code></em>+1</code> for
an input outside the range</td><td><code class="literal">width_bucket(5.35, 0.024, 10.06, 5)</code></td><td><code class="literal">3</code></td></tr><tr><td><code class="literal"><code class="function">width_bucket(<em class="parameter"><code>operand</code></em> <code class="type">numeric</code>, <em class="parameter"><code>b1</code></em> <code class="type">numeric</code>, <em class="parameter"><code>b2</code></em> <code class="type">numeric</code>, <em class="parameter"><code>count</code></em> <code class="type">int</code>)</code></code></td><td><code class="type">int</code></td><td>return the bucket number to which <em class="parameter"><code>operand</code></em> would
be assigned in a histogram having <em class="parameter"><code>count</code></em> equal-width
buckets spanning the range <em class="parameter"><code>b1</code></em> to <em class="parameter"><code>b2</code></em>;
returns <code class="literal">0</code> or <code class="literal"><em class="parameter"><code>count</code></em>+1</code> for
an input outside the range</td><td><code class="literal">width_bucket(5.35, 0.024, 10.06, 5)</code></td><td><code class="literal">3</code></td></tr><tr><td><code class="literal"><code class="function">width_bucket(<em class="parameter"><code>operand</code></em> <code class="type">anyelement</code>, <em class="parameter"><code>thresholds</code></em> <code class="type">anyarray</code>)</code></code></td><td><code class="type">int</code></td><td>return the bucket number to which <em class="parameter"><code>operand</code></em> would
be assigned given an array listing the lower bounds of the buckets;
returns <code class="literal">0</code> for an input less than the first lower bound;
the <em class="parameter"><code>thresholds</code></em> array <span class="emphasis"><em>must be sorted</em></span>,
smallest first, or unexpected results will be obtained</td><td><code class="literal">width_bucket(now(), array['yesterday', 'today', 'tomorrow']::timestamptz[])</code></td><td><code class="literal">2</code></td></tr></tbody></table></div></div><br class="table-break" /><p>
<a class="xref" href="functions-math.html#FUNCTIONS-MATH-RANDOM-TABLE" title="Table 9.6. Random Functions">Table 9.6</a> shows functions for
generating random numbers.
</p><div class="table" id="FUNCTIONS-MATH-RANDOM-TABLE"><p class="title"><strong>Table 9.6. Random Functions</strong></p><div class="table-contents"><table class="table" summary="Random Functions" border="1"><colgroup><col /><col /><col /></colgroup><thead><tr><th>Function</th><th>Return Type</th><th>Description</th></tr></thead><tbody><tr><td>
<a id="id-1.5.8.8.9.2.2.1.1.1" class="indexterm"></a>
<code class="literal"><code class="function">random()</code></code>
</td><td><code class="type">dp</code></td><td>random value in the range 0.0 <= x < 1.0</td></tr><tr><td>
<a id="id-1.5.8.8.9.2.2.2.1.1" class="indexterm"></a>
<code class="literal"><code class="function">setseed(<code class="type">dp</code>)</code></code>
</td><td><code class="type">void</code></td><td>set seed for subsequent <code class="literal">random()</code> calls (value between -1.0 and
1.0, inclusive)</td></tr></tbody></table></div></div><br class="table-break" /><p>
The characteristics of the values returned by
<code class="literal"><code class="function">random()</code></code> depend
on the system implementation. It is not suitable for cryptographic
applications; see <a class="xref" href="pgcrypto.html" title="F.25. pgcrypto">pgcrypto</a> module for an alternative.
</p><p>
Finally, <a class="xref" href="functions-math.html#FUNCTIONS-MATH-TRIG-TABLE" title="Table 9.7. Trigonometric Functions">Table 9.7</a> shows the
available trigonometric functions. All trigonometric functions
take arguments and return values of type <code class="type">double
precision</code>. Each of the trigonometric functions comes in
two variants, one that measures angles in radians and one that
measures angles in degrees.
</p><div class="table" id="FUNCTIONS-MATH-TRIG-TABLE"><p class="title"><strong>Table 9.7. Trigonometric Functions</strong></p><div class="table-contents"><table class="table" summary="Trigonometric Functions" border="1"><colgroup><col /><col /><col /></colgroup><thead><tr><th>Function (radians)</th><th>Function (degrees)</th><th>Description</th></tr></thead><tbody><tr><td>
<a id="id-1.5.8.8.12.2.2.1.1.1" class="indexterm"></a><code class="literal"><code class="function">acos(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>
<a id="id-1.5.8.8.12.2.2.1.2.1" class="indexterm"></a><code class="literal"><code class="function">acosd(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>inverse cosine</td></tr><tr><td>
<a id="id-1.5.8.8.12.2.2.2.1.1" class="indexterm"></a>
<code class="literal"><code class="function">asin(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>
<a id="id-1.5.8.8.12.2.2.2.2.1" class="indexterm"></a>
<code class="literal"><code class="function">asind(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>inverse sine</td></tr><tr><td>
<a id="id-1.5.8.8.12.2.2.3.1.1" class="indexterm"></a>
<code class="literal"><code class="function">atan(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>
<a id="id-1.5.8.8.12.2.2.3.2.1" class="indexterm"></a>
<code class="literal"><code class="function">atand(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>inverse tangent</td></tr><tr><td>
<a id="id-1.5.8.8.12.2.2.4.1.1" class="indexterm"></a>
<code class="literal"><code class="function">atan2(<em class="replaceable"><code>y</code></em>,
<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>
<a id="id-1.5.8.8.12.2.2.4.2.1" class="indexterm"></a>
<code class="literal"><code class="function">atan2d(<em class="replaceable"><code>y</code></em>,
<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>inverse tangent of
<code class="literal"><em class="replaceable"><code>y</code></em>/<em class="replaceable"><code>x</code></em></code></td></tr><tr><td>
<a id="id-1.5.8.8.12.2.2.5.1.1" class="indexterm"></a>
<code class="literal"><code class="function">cos(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>
<a id="id-1.5.8.8.12.2.2.5.2.1" class="indexterm"></a>
<code class="literal"><code class="function">cosd(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>cosine</td></tr><tr><td>
<a id="id-1.5.8.8.12.2.2.6.1.1" class="indexterm"></a>
<code class="literal"><code class="function">cot(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>
<a id="id-1.5.8.8.12.2.2.6.2.1" class="indexterm"></a>
<code class="literal"><code class="function">cotd(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>cotangent</td></tr><tr><td>
<a id="id-1.5.8.8.12.2.2.7.1.1" class="indexterm"></a>
<code class="literal"><code class="function">sin(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>
<a id="id-1.5.8.8.12.2.2.7.2.1" class="indexterm"></a>
<code class="literal"><code class="function">sind(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>sine</td></tr><tr><td>
<a id="id-1.5.8.8.12.2.2.8.1.1" class="indexterm"></a>
<code class="literal"><code class="function">tan(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>
<a id="id-1.5.8.8.12.2.2.8.2.1" class="indexterm"></a>
<code class="literal"><code class="function">tand(<em class="replaceable"><code>x</code></em>)</code></code>
</td><td>tangent</td></tr></tbody></table></div></div><br class="table-break" /><div class="note"><h3 class="title">Note</h3><p>
Another way to work with angles measured in degrees is to use the unit
transformation functions <code class="literal"><code class="function">radians()</code></code>
and <code class="literal"><code class="function">degrees()</code></code> shown earlier.
However, using the degree-based trigonometric functions is preferred,
as that way avoids round-off error for special cases such
as <code class="literal">sind(30)</code>.
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