diff --git a/Doc/Sd1/CoreClasses/coreClasses.xml b/Doc/Sd1/CoreClasses/coreClasses.xml
index cacd2d633d78aeeae26655a56cea57c339366759..bc5e7ae780d6e6dadaa75eb689429689a4285717 100644
--- a/Doc/Sd1/CoreClasses/coreClasses.xml
+++ b/Doc/Sd1/CoreClasses/coreClasses.xml
@@ -15,8 +15,8 @@
<abstract>
<para>Working with class <classname>String</classname>.</para>
- <para>Pitfalls when using operator <code language="java">==</code>
- </para>
+ <para>Pitfalls when using operator <code
+ language="java">==</code></para>
<para>Using <methodname>equals(...)</methodname>.</para>
</abstract>
@@ -652,7 +652,228 @@ hashcode of BB: 2112</screen></td>
<para><classname
xlink:href="https://docs.oracle.com/en/java/javase/17/docs/api/java.base/java/lang/Math.html">Math</classname>
is yet another class belonging to the core set of the <xref
- linkend="glo_Java"/> programing language.</para>
+ linkend="glo_Java"/> programing language. We take a tour on selected
+ methods:</para>
+
+ <figure xml:id="sd1_coreclasses_fig_mathSine">
+ <title><classname>Math</classname>.<methodname>sin(double
+ x)</methodname></title>
+
+ <informaltable border="1">
+ <colgroup width="50%"/>
+
+ <colgroup width="38%"/>
+
+ <colgroup width="12%"/>
+
+ <tr>
+ <th>Code</th>
+
+ <th>Result</th>
+
+ <th>Math notation</th>
+ </tr>
+
+ <tr>
+ <td valign="top"><programlisting language="java">final double x = 90;
+final double y = Math.sin(x);
+System.out.println(y + " == sin(" + x + ")");</programlisting></td>
+
+ <td valign="top"><screen>0.8939966636005579 == sin(90.0) </screen></td>
+
+ <td valign="top"><informalequation>
+ <m:math display="block">
+ <m:mrow>
+ <m:mi>y</m:mi>
+
+ <m:mo>=</m:mo>
+
+ <m:mrow>
+ <m:mi>sin</m:mi>
+
+ <m:mo>â¡</m:mo>
+
+ <m:mi>x</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:math>
+ </informalequation></td>
+ </tr>
+ </informaltable>
+ </figure>
+
+ <qandaset defaultlabel="qanda" xml:id="sw1QandaMathSine">
+ <title>Common pitfall using trigonometric functions</title>
+
+ <qandadiv>
+ <qandaentry>
+ <question>
+ <para>We reconsider <xref
+ linkend="sd1_coreclasses_fig_mathSine"/>. Did you expect a value
+ of <code>0.8939966636005579</code> corresponding to an angle of
+ 90° here? Discuss the underlying problem.</para>
+ </question>
+
+ <answer>
+ <para>The mathematically inclined reader may have expected a
+ result of <code>1.000...</code> corresponding to a right angle of
+ 90° rather than <code>0.893...</code>.</para>
+
+ <para>This is a common misconception: At school you were probably
+ using so called <quote>degrees</quote> ranging from 0° to 360° for
+ describing angle values. In Mathematics however trigonometric
+ functions are being defined as power series e.g.:</para>
+
+ <informalequation>
+ <m:math display="block">
+ <m:mrow>
+ <m:mrow>
+ <m:mi>sin</m:mi>
+
+ <m:mo>â¡</m:mo>
+
+ <m:mi>x</m:mi>
+ </m:mrow>
+
+ <m:mo>=</m:mo>
+
+ <m:mi>x</m:mi>
+
+ <m:mo>-</m:mo>
+
+ <m:mfrac>
+ <m:msup>
+ <m:mi>x</m:mi>
+
+ <m:mi>3</m:mi>
+ </m:msup>
+
+ <m:mi>3!</m:mi>
+ </m:mfrac>
+
+ <m:mo>+</m:mo>
+
+ <m:mfrac>
+ <m:msup>
+ <m:mi>x</m:mi>
+
+ <m:mi>5</m:mi>
+ </m:msup>
+
+ <m:mi>5!</m:mi>
+ </m:mfrac>
+
+ <m:mo>+</m:mo>
+
+ <m:mi>...</m:mi>
+
+ <m:mo>=</m:mo>
+
+ <m:mrow>
+ <m:munderover>
+ <m:mo>∑</m:mo>
+
+ <m:mi>n = 0</m:mi>
+
+ <m:mi mathvariant="normal">∞</m:mi>
+ </m:munderover>
+
+ <m:mfrac>
+ <m:mrow>
+ <m:msup>
+ <m:mrow>
+ <m:mo>(</m:mo>
+
+ <m:mi>-1</m:mi>
+
+ <m:mo>)</m:mo>
+ </m:mrow>
+
+ <m:mi>n</m:mi>
+ </m:msup>
+
+ <m:mo>â¢</m:mo>
+
+ <m:msup>
+ <m:mi>x</m:mi>
+
+ <m:mrow>
+ <m:mi>2n</m:mi>
+
+ <m:mo>+</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:msup>
+ </m:mrow>
+
+ <m:mrow>
+ <m:mo>(</m:mo>
+
+ <m:mrow>
+ <m:mi>2n</m:mi>
+
+ <m:mo>+</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+
+ <m:mo>)</m:mo>
+
+ <m:mi>!</m:mi>
+ </m:mrow>
+ </m:mfrac>
+ </m:mrow>
+ </m:mrow>
+ </m:math>
+ </informalequation>
+
+ <para>As an immediate consequence describing a full circle of
+ angle values the variable x here is ranging from 0 to
+ <inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:mi>2</m:mi>
+
+ <m:mo>â¢</m:mo>
+
+ <m:mi>Ï€</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation> rather than from 0° to 360°. This angle unit
+ is called radians. If you still want to use degrees you will have
+ to convert these to radians beforehand by multiplying with
+ <inlineequation>
+ <m:math display="inline">
+ <m:mfrac bevelled="true">
+ <m:mrow>
+ <m:mi>2</m:mi>
+
+ <m:mo>â¢</m:mo>
+
+ <m:mi>Ï€</m:mi>
+ </m:mrow>
+
+ <m:mi>360°</m:mi>
+ </m:mfrac>
+ </m:math>
+ </inlineequation> or simply <inlineequation>
+ <m:math display="inline">
+ <m:mfrac bevelled="true">
+ <m:mi>Ï€</m:mi>
+
+ <m:mi>180</m:mi>
+ </m:mfrac>
+ </m:math>
+ </inlineequation>:</para>
+
+ <programlisting language="java">final double x = 90;
+final double y = Math.sin(x * Math.PI / 180); //converting degrees to radians
+System.out.println(y + " == sin(" + x + ")");</programlisting>
+ </answer>
+ </qandaentry>
+ </qandadiv>
+ </qandaset>
<qandaset defaultlabel="qanda" xml:id="sw1QandaCircleAreaMathPackage">
<title>Using constants from <classname
@@ -677,12 +898,12 @@ hashcode of BB: 2112</screen></td>
}</programlisting>
<para>You may have wondered why you had to punch in the value of
- <inlineequation>
+ such an important constant as <inlineequation>
<m:math display="inline">
<m:mi>Ï€</m:mi>
</m:math>
- </inlineequation> yourself. Actually <xref linkend="glo_Java"/>
- predefines constants in <classname
+ </inlineequation> by yourself. Actually <xref
+ linkend="glo_Java"/> predefines constants in <classname
xlink:href="https://docs.oracle.com/en/java/javase/17/docs/api/java.base/java/lang/Math.html">java.lang.Math</classname>
class. Read its documentation to rewrite your code thereby
replacing your own variable <code language="java">pi</code>'s