Exemple : Utilisation des angles polaires

Fonctions > Graphique > Exemple : Utilisation des angles polaires

1. Définissez deux vecteurs de longueur égale, décrivant les coordonnées X et Y.

2. Utilisez les fonctions angle et atan2 pour obtenir les angles correspondants des coordonnées X et Y.

atan2 n'est pas définie à (0,0).

3. Calculez le rayon vecteur à l'aide de la coordonnée X et tracez le résultat.

<region id="ID0EVL4W" top="556.80000000000007" left="19.200000000000003" height="331.19999999999993" width="331.19999999999993" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <polarPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="41">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <graph-size width="231.2" height="231.2" />
      <axes>
        <angularAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="360">
          <axisLine position="origin" positionticmark="6" legendWidth="36.1266666666667" />
          <axisGrid>
            <gridFrequency>13</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math resultRef="42">
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">a</id>
              </math>
            </plotEquation>
          </plotEquations>
          <angularDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </angularDomain>
        </angularAxis>
        <radialAxis rank="1" legend-position="PlotBoundaryRight" start="0" end="5">
          <axisLine position="origin" positionticmark="2" legendWidth="59.48" />
          <axisGrid>
            <gridFrequency>6</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math resultRef="45">
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">r</id>
              </math>
              <math resultRef="46">
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <radialDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="44">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </radialDomain>
        </radialAxis>
      </axes>
    </polarPlot>
  </plot>
</region>

4. Calculez le rayon à l'aide des résultats de la fonction atan2, tracez-le, et comparez-le au tracé précédent.

<region id="ID0EXN4W" top="1036.8000000000002" left="38.400000000000006" height="331.2" width="331.2" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <polarPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="53">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <graph-size width="231.2" height="231.2" />
      <axes>
        <angularAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="360">
          <axisLine position="origin" positionticmark="6" legendWidth="35.3633333333333" />
          <axisGrid>
            <gridFrequency>13</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math resultRef="54">
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">b</id>
              </math>
            </plotEquation>
          </plotEquations>
          <angularDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </angularDomain>
        </angularAxis>
        <radialAxis rank="1" legend-position="PlotBoundaryRight" start="0" end="5">
          <axisLine position="origin" positionticmark="2" legendWidth="67.46" />
          <axisGrid>
            <gridFrequency>6</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math resultRef="57">
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">r2</id>
              </math>
              <math resultRef="58">
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <radialDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="56">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </radialDomain>
        </radialAxis>
      </axes>
    </polarPlot>
  </plot>
</region>

Les deux tracés sont identiques.

Rubriques associées

Angles polaires

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