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  <resource>
  <id>7050</id>
  <path>/www/nrich/html/content/id/7050/</path>
  <resourceTypeID>1</resourceTypeID>
  <last_published>2011-02-01T00:00:01</last_published>
  <indexXML>&lt;mdoxml xmlns:ns0=&quot;http://nrich.maths.org/mdo&quot; version=&quot;1.0&quot;&gt;
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      &lt;a href=&quot;http://nrich.maths.org/2845&amp;amp;part=&quot;&gt;Warm-up
problem&lt;/a&gt;
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  &lt;div&gt;
    &lt;div&gt;&amp;#160;&lt;/div&gt;
    &lt;table border=&quot;0&quot;&gt;
      &lt;tbody&gt;
        &lt;tr&gt;
          &lt;td&gt;
            &lt;mdo:image alt=&quot;&quot; height=&quot;302&quot; src=&quot;Diagram.png&quot; width=&quot;314&quot; /&gt;
          &lt;/td&gt;
          &lt;td&gt;In this diagram $O$ is the centre of a unit circle. Use it to
find a trigonometrical relationship between $A$ and $2A$.&lt;/td&gt;
        &lt;/tr&gt;
      &lt;/tbody&gt;
    &lt;/table&gt;
    &lt;div&gt;&amp;#160;&lt;/div&gt;
    &lt;div&gt;&amp;#160;&lt;/div&gt;
    &lt;div&gt;&amp;#160;&lt;/div&gt;
  &lt;/div&gt;
  &lt;div class=&quot;framework&quot;&gt;
    &lt;span style=&quot;font-style: italic;&quot;&gt;Did you
know ... ?&lt;/span&gt;
    &lt;br /&gt;
    &lt;br /&gt;
Trigonometrical expressions can often be derived algebraically or
geometrically. In more advanced applications the functions of
trigonometry are defined as infinite power series rather than
geometric ratios.&lt;/div&gt;
  &lt;br /&gt;
&lt;/mdoxml&gt;
</indexXML>
  <solutionXML>&lt;?xml version=&quot;1.0&quot; encoding=&quot;UTF-8&quot;?&gt;
&lt;mdoxml version=&quot;1.0&quot;&gt;This image, making use of results from circle theorems, says it
all!&lt;br&gt;&lt;/br&gt;
 &lt;br&gt;&lt;/br&gt;
 &lt;mdo:image height=&quot;322&quot; width=&quot;328&quot; src=&quot;solution.jpg&quot; alt=&quot;solution picture&quot;&gt;&lt;/mdo:image&gt;&lt;br&gt;&lt;/br&gt;
 &lt;br&gt;&lt;/br&gt;
 &lt;br&gt;&lt;/br&gt;&lt;/mdoxml&gt;</solutionXML>
  <noteXML/>
  <clueXML/>
  <canonXML>&lt;?xml version=&quot;1.0&quot; encoding=&quot;UTF-8&quot;?&gt;
&lt;mdoxml version=&quot;1.0&quot;&gt;This image, making use of results from circle theorems, says it
all!&lt;br&gt;&lt;/br&gt;
 &lt;br&gt;&lt;/br&gt;
 &lt;mdo:image height=&quot;322&quot; width=&quot;328&quot; src=&quot;solution.jpg&quot; alt=&quot;solution picture&quot;&gt;&lt;/mdo:image&gt;&lt;br&gt;&lt;/br&gt;
 &lt;br&gt;&lt;/br&gt;
 &lt;br&gt;&lt;/br&gt;&lt;/mdoxml&gt;</canonXML>
  <end_user_role>2</end_user_role>
  <difficulty>3</difficulty>
  <keystage1>0</keystage1>
  <keystage2>0</keystage2>
  <keystage3>0</keystage3>
  <keystage4>1</keystage4>
  <keystage4plus>1</keystage4plus>
  <title>Weekly Challenge 21: Trig identity</title>
  <description>A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.</description>
  <spec_group>Collections
    <specifier>Weekly Challenge</specifier>
  </spec_group>
  <spec_group>Admin
    <specifier>Stage 5 - Core Mapping</specifier>
  </spec_group>
  <spec_group>Stage 5 Core Mapping Document
    <specifier>Trigonometry A2</specifier>
  </spec_group>
  <spec_group>Secondary Mapping Document
    <specifier>DisplayCabinet</specifier>
  </spec_group>
</resource>