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Commit 7670ff04 authored by Goik Martin's avatar Goik Martin
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Adding sine degree radian exercise

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Doc/Sd1/CoreClasses/coreClasses.xml
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......@@ -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>⁡</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>⁡</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>⁢</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>⁢</m:mo>
<m:mi>π</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>⁢</m:mo>
<m:mi>π</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>π</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>π</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
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