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<h4><a name="uk.ac.starlink.ttools.func.Maths">10.5.15 Maths</a></h4>
<p>Standard mathematical and trigonometric functions.
Trigonometric functions work with angles in radians.
</p>
<p>
<dl>
<dt><strong><code>sin( theta )</code></strong></dt>
<dd>Sine of an angle.
<ul>
<li><code>theta</code> <em>(floating point)</em>: an angle, in radians.
</li>
<li>return value <em>(floating point)</em>: the sine of the argument.
</li>
</ul>
</dd>
<dt><strong><code>cos( theta )</code></strong></dt>
<dd>Cosine of an angle.
<ul>
<li><code>theta</code> <em>(floating point)</em>: an angle, in radians.
</li>
<li>return value <em>(floating point)</em>: the cosine of the argument.
</li>
</ul>
</dd>
<dt><strong><code>tan( theta )</code></strong></dt>
<dd>Tangent of an angle.
<ul>
<li><code>theta</code> <em>(floating point)</em>: an angle, in radians.
</li>
<li>return value <em>(floating point)</em>: the tangent of the argument.
</li>
</ul>
</dd>
<dt><strong><code>asin( x )</code></strong></dt>
<dd>Arc sine of an angle.
The result is in the range of -<em>pi</em>/2 through
<em>pi</em>/2.
<ul>
<li><code>x</code> <em>(floating point)</em>: the value whose arc sine is to be returned.
</li>
<li>return value <em>(floating point)</em>: the arc sine of the argument (radians)
</li>
</ul>
</dd>
<dt><strong><code>acos( x )</code></strong></dt>
<dd>Arc cosine of an angle.
The result is in the range of 0.0 through <em>pi</em>.
<ul>
<li><code>x</code> <em>(floating point)</em>: the value whose arc cosine is to be returned.
</li>
<li>return value <em>(floating point)</em>: the arc cosine of the argument (radians)
</li>
</ul>
</dd>
<dt><strong><code>atan( x )</code></strong></dt>
<dd>Arc tangent of an angle.
The result is in the range of -<em>pi</em>/2 through <em>pi</em>/2.
<ul>
<li><code>x</code> <em>(floating point)</em>: the value whose arc tangent is to be returned.
</li>
<li>return value <em>(floating point)</em>: the arc tangent of the argument (radians)
</li>
</ul>
</dd>
<dt><strong><code>exp( x )</code></strong></dt>
<dd>Euler's number <em>e</em> raised to a power.
<ul>
<li><code>x</code> <em>(floating point)</em>: the exponent to raise <em>e</em> to.
</li>
<li>return value <em>(floating point)</em>: the value <em>e</em><sup>x</sup>,
where <em>e</em> is the base of the natural logarithms.
</li>
</ul>
</dd>
<dt><strong><code>log10( x )</code></strong></dt>
<dd>Logarithm to base 10.
<ul>
<li><code>x</code> <em>(floating point)</em>: argument
</li>
<li>return value <em>(floating point)</em>: log<sub>10</sub>(x)
</li>
</ul>
</dd>
<dt><strong><code>ln( x )</code></strong></dt>
<dd>Natural logarithm.
<ul>
<li><code>x</code> <em>(floating point)</em>: argument
</li>
<li>return value <em>(floating point)</em>: log<sub>e</sub>(x)
</li>
</ul>
</dd>
<dt><strong><code>sqrt( x )</code></strong></dt>
<dd>Square root.
The result is correctly rounded and positive.
<ul>
<li><code>x</code> <em>(floating point)</em>: a value.
</li>
<li>return value <em>(floating point)</em>: the positive square root of <code>x</code>.
If the argument is NaN or less than zero, the result is NaN.
</li>
</ul>
</dd>
<dt><strong><code>hypot( xs, ... )</code></strong></dt>
<dd>Returns the square root of the sum of squares of its arguments.
In the 2-argument case, doing it like this may avoid intermediate
overflow or underflow.
<ul>
<li><code>xs</code> <em>(floating point, one or more)</em>: one or more numeric values
</li>
<li>return value <em>(floating point)</em>: sqare root of sum of squares of arguments
</li>
</ul>
</dd>
<dt><strong><code>atan2( y, x )</code></strong></dt>
<dd>Converts rectangular coordinates (<code>x</code>,<code>y</code>)
to polar (<code>r</code>,<code>theta</code>).
This method computes the phase
<code>theta</code> by computing an arc tangent
of <code>y/x</code> in the range of -<em>pi</em> to <em>pi</em>.
<ul>
<li><code>y</code> <em>(floating point)</em>: the ordinate coordinate
</li>
<li><code>x</code> <em>(floating point)</em>: the abscissa coordinate
</li>
<li>return value <em>(floating point)</em>: the <code>theta</code> component (radians) of the point
(<code>r</code>,<code>theta</code>)
in polar coordinates that corresponds to the point
(<code>x</code>,<code>y</code>) in Cartesian coordinates.
</li>
</ul>
</dd>
<dt><strong><code>pow( a, b )</code></strong></dt>
<dd>Exponentiation.
The result is the value of the first argument raised to
the power of the second argument.
<ul>
<li><code>a</code> <em>(floating point)</em>: the base.
</li>
<li><code>b</code> <em>(floating point)</em>: the exponent.
</li>
<li>return value <em>(floating point)</em>: the value <code>a<sup>b</sup></code>.
</li>
</ul>
</dd>
<dt><strong><code>sinh( x )</code></strong></dt>
<dd>Hyperbolic sine.
<ul>
<li><code>x</code> <em>(floating point)</em>: parameter
</li>
<li>return value <em>(floating point)</em>: result
</li>
</ul>
</dd>
<dt><strong><code>cosh( x )</code></strong></dt>
<dd>Hyperbolic cosine.
<ul>
<li><code>x</code> <em>(floating point)</em>: parameter
</li>
<li>return value <em>(floating point)</em>: result
</li>
</ul>
</dd>
<dt><strong><code>tanh( x )</code></strong></dt>
<dd>Hyperbolic tangent.
<ul>
<li><code>x</code> <em>(floating point)</em>: parameter
</li>
<li>return value <em>(floating point)</em>: result
</li>
</ul>
</dd>
<dt><strong><code>asinh( x )</code></strong></dt>
<dd>Inverse hyperbolic sine.
<ul>
<li><code>x</code> <em>(floating point)</em>: parameter
</li>
<li>return value <em>(floating point)</em>: result
</li>
</ul>
</dd>
<dt><strong><code>acosh( x )</code></strong></dt>
<dd>Inverse hyperbolic cosine.
<ul>
<li><code>x</code> <em>(floating point)</em>: parameter
</li>
<li>return value <em>(floating point)</em>: result
</li>
</ul>
</dd>
<dt><strong><code>atanh( x )</code></strong></dt>
<dd>Inverse hyperbolic tangent.
<ul>
<li><code>x</code> <em>(floating point)</em>: parameter
</li>
<li>return value <em>(floating point)</em>: result
</li>
</ul>
</dd>
<dt><strong><code>E</code></strong></dt>
<dd>Euler's number <em>e</em>, the base of natural logarithms.
<ul></ul>
</dd>
<dt><strong><code>PI</code></strong></dt>
<dd><em>Pi</em>, the ratio of the circumference of a circle to its diameter.
<ul></ul>
</dd>
<dt><strong><code>Infinity</code></strong></dt>
<dd>Positive infinite floating point value.
<ul></ul>
</dd>
<dt><strong><code>NaN</code></strong></dt>
<dd>Not-a-Number floating point value.
Use with care; arithmetic and logical operations behave in strange
ways near NaN (for instance, <code>NaN!=NaN</code>).
For most purposes this is equivalent to the blank value.
<ul></ul>
</dd>
<dt><strong><code>RANDOM</code></strong></dt>
<dd>Evaluates to a random number in the range 0<=x<1.
This is different for each cell of the table.
The quality of the randomness may not be particularly good.
<ul></ul>
</dd>
</dl>
</p>
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