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Laura.2mdc: Revertidas las ediciones realizadas por 190.14.227.187 (Talk); a la última edición de 213.97.196.225
2010-05-25T08:36:53Z
<p>Revertidas las ediciones realizadas por <a href="/Especial:Contributions/190.14.227.187.html" title="Especial:Contributions/190.14.227.187">190.14.227.187</a> (<a href="/Usuario_Discusi%C3%B3n:190.14.227.187.html" title="Usuario Discusión:190.14.227.187">Talk</a>); a la última edición de <a href="/index.php?title=Usuario:213.97.196.225&action=edit" class="new" title="Usuario:213.97.196.225">213.97.196.225</a></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 08:36 25 may 2010</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><<del style="color: red; font-weight: bold; text-decoration: none;">zulli=tu corazonada</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><<ins style="color: red; font-weight: bold; text-decoration: none;">br/></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, puedes encontrar la respeusta en [[Reducción de las razones trigonometricas]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, puedes encontrar la respeusta en [[Reducción de las razones trigonometricas]].</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">'''Texto en negrita'''</del></div></td><td colspan="2"> </td></tr>
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Laura.2mdc
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190.14.227.187 en 16:57 24 may 2010
2010-05-24T16:57:19Z
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<td colspan='2' style="background-color: white; color:black;">Revisión de 16:57 24 may 2010</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><<del style="color: red; font-weight: bold; text-decoration: none;">br/></del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><<ins style="color: red; font-weight: bold; text-decoration: none;">zulli=tu corazonada</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, puedes encontrar la respeusta en [[Reducción de las razones trigonometricas]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, puedes encontrar la respeusta en [[Reducción de las razones trigonometricas]].</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">'''Texto en negrita'''</ins></div></td></tr>
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190.14.227.187
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213.97.196.225 en 14:36 10 ene 2007
2007-01-10T14:36:47Z
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<td colspan='2' style="background-color: white; color:black;">Revisión de 14:36 10 ene 2007</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, la <del style="color: red; font-weight: bold; text-decoration: none;">respuesta la tienes </del>[[Reducción de las razones trigonometricas<del style="color: red; font-weight: bold; text-decoration: none;">|en esta sección</del>]].</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, <ins style="color: red; font-weight: bold; text-decoration: none;">puedes encontrar </ins>la <ins style="color: red; font-weight: bold; text-decoration: none;">respeusta en </ins>[[Reducción de las razones trigonometricas]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
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213.97.196.225
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213.97.196.225 en 14:35 10 ene 2007
2007-01-10T14:35:46Z
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<td colspan='2' style="background-color: white; color:black;">Revisión de 14:35 10 ene 2007</td>
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<tr><td colspan="2" class="diff-lineno">Línea 233:</td>
<td colspan="2" class="diff-lineno">Línea 233:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, la respuesta la tienes [[Reducción de las razones</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, la respuesta la tienes [[Reducción de las razones trigonometricas|en esta sección]].</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>trigonometricas | en esta sección]].</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
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213.97.196.225
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213.97.196.225 en 14:34 10 ene 2007
2007-01-10T14:34:35Z
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<tr><td colspan="2" class="diff-lineno">Línea 234:</td>
<td colspan="2" class="diff-lineno">Línea 234:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, la respuesta la tienes [[Reducción de las razones</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, la respuesta la tienes [[Reducción de las razones</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>trigonometricas|en esta sección]].</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>trigonometricas | en esta sección]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
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Fjmolina en 13:51 10 ene 2007
2007-01-10T13:51:12Z
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, la respuesta la tienes [[Reducción de las razones trigonometricas|en esta sección]].</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Si te preguntas porque esto es así, la respuesta la tienes [[Reducción de las razones</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>trigonometricas|en esta sección]].</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
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Fjmolina
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Fjmolina en 13:05 10 ene 2007
2007-01-10T13:05:18Z
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">La segunda igualdad es cierta por las relaciones entre las razones trigonometricas de</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\alpha</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&nbsp; y &nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">-\alpha</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math>:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\mathrm{cos}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, -\alpha \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, = \, \mathrm{cos}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, \alpha \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\mathrm{sen}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, -\alpha \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, = \, -\mathrm{sen}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, \alpha \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Si te preguntas porque esto es así, la respuesta la tienes [[Reducción de las razones trigonometricas|en esta sección]].</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
</table>
Fjmolina
http://wikillerato.org/index.php?title=Razones_trigonom%C3%A9tricas_de_la_suma_y_diferencia_de_%C3%A1ngulos&diff=2797&oldid=prev
Fjmolina en 01:48 31 dic 2006
2006-12-31T01:48:20Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 01:48 31 dic 2006</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Línea 1:</td>
<td colspan="2" class="diff-lineno">Línea 1:</td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Se puede demostrar que dados dos angulos &nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\alpha</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&nbsp; y &nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\beta</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">, el seno de su suma viene dado por la formula:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 81:</td>
<td colspan="2" class="diff-lineno">Línea 93:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></center></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">El coseno de la suma de los angulos &nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\alpha</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&nbsp; y &nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\beta</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&nbsp; viene dado por la formula:</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
</table>
Fjmolina
http://wikillerato.org/index.php?title=Razones_trigonom%C3%A9tricas_de_la_suma_y_diferencia_de_%C3%A1ngulos&diff=2796&oldid=prev
83.61.53.15 en 01:42 31 dic 2006
2006-12-31T01:42:33Z
<p></p>
<a href="http://wikillerato.org/index.php?title=Razones_trigonom%C3%A9tricas_de_la_suma_y_diferencia_de_%C3%A1ngulos&diff=2796&oldid=2795">(Diferencias entre revisiones)</a>
83.61.53.15
http://wikillerato.org/index.php?title=Razones_trigonom%C3%A9tricas_de_la_suma_y_diferencia_de_%C3%A1ngulos&diff=2795&oldid=prev
83.61.53.15 en 01:41 31 dic 2006
2006-12-31T01:41:51Z
<p></p>
<p><b>Página nueva</b></p><div>Dado un triángulo rectángulo, podemos estudiar las razones o proporciones entre sus<br />
lados.<br />
<br />
<br/><br />
<br />
<center><br />
[[Image:triangulo.gif]]<br />
</center><br />
<br />
<br/><br />
<br />
Estas razones las definimos asociadas a cada uno de sus angulos de la siguiente<br />
forma:<br />
<br />
El seno de un ángulo, es la razon entre su cateto opuesto y la hipotenusa. Su inversa es<br />
la cosecante:<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{sen} \, \alpha = \frac{\makebox{cateto opuesto}}{\makebox{hipotenusa}}<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{cosec} \, \alpha = \frac{\makebox{hipotenusa}}{\makebox{cateto opuesto}}<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
El coseno de un ángulo, es la razon entre su cateto contiguo y la hipotenusa. Su inversa<br />
es la secante:<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\cos \alpha = \frac{\makebox{cateto contiguo}}{\makebox{hipotenusa}}<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\sec \alpha = \frac{\makebox{hipotenusa}}{\makebox{cateto contiguo}}<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
La tangente de un ángulo, es la razon entre su cateto opuesto y su cateto contiguo. Su<br />
inversa es la contangente:<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{tg} \, \alpha = \frac{\makebox{cateto opuesto}}{\makebox{cateto contiguo}}<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{cotg} \, \alpha = \frac{\makebox{cateto contiguo}}{\makebox{cateto opuesto}}<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
Para el estudio de las razones trigonometricas se suele considerar el angulo &nbsp;<br />
<math><br />
\alpha<br />
</math><br />
&nbsp; que forma el eje &nbsp;<br />
<math><br />
X<br />
</math><br />
&nbsp; con el radio de una circunferencia de radio &nbsp;<br />
<math><br />
1<br />
</math><br />
&nbsp; y centrada en el origen de coordenadas. A esta circunferencia se le llama<br />
circunferencia goniometrica.<br />
<br />
<br/><br />
<br />
<center><br />
[[Image:circulo.gif]]<br />
</center><br />
<br />
<br/><br />
<br />
En este caso<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{sen} \, \alpha = y \qquad \mathrm{cosec} \, \alpha = \frac{1}{y} \qquad<br />
<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\cos \alpha = x \qquad \sec \alpha = \frac{1}{x}<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{tg} \, \alpha = \frac{y}{x} \qquad \mathrm{cotg} \, \alpha = \frac{x}{y}<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
El angulo &nbsp;<br />
<math><br />
\alpha<br />
</math><br />
&nbsp; aumenta sii movemos el punto &nbsp;<br />
<math><br />
P<br />
</math><br />
&nbsp; en la circunferencia de manera que el radio &nbsp;<br />
<math><br />
\overline{OP}<br />
</math><br />
&nbsp; gire en sentido contrario al de las las agujas del reloj.<br />
<br />
<br/><br />
<br />
Si &nbsp;<br />
<math><br />
P<br />
</math><br />
&nbsp; esta a la derecha del eje &nbsp;<br />
<math><br />
Y,<br />
</math><br />
&nbsp; entonces &nbsp;<br />
<math><br />
x > 0.<br />
</math><br />
&nbsp; En caso contrario, se tiene que &nbsp;<br />
<math><br />
x < 0.<br />
</math><br />
&nbsp; Si &nbsp;<br />
<math><br />
P<br />
</math><br />
&nbsp; esta por encima del eje &nbsp;<br />
<math><br />
X,<br />
</math><br />
&nbsp; entonces &nbsp;<br />
<math><br />
y > 0.<br />
</math><br />
&nbsp; En caso contrario, se tiene que &nbsp;<br />
<math><br />
y < 0.<br />
</math><br />
<br />
<br/><br />
<br />
Los ejes de coordenadas dividen la circunferencia goniometrica en cuatro cuadrantes. El<br />
signo de las razones de un angulo &nbsp;<br />
<math><br />
\alpha<br />
</math><br />
&nbsp; depende de en que cuadrante este situado &nbsp;<br />
<math><br />
P<br />
</math><br />
. Todas las posibilidades estan recogidas en la tabla siguiente:<br />
<br />
<br/><br />
<br />
<center><br />
[[Image:tabla.gif]]<br />
</center><br />
<br />
%% }}}<br />
%% {{{ =suma y diferencia de angulos <br />
<br />
<center><br />
<math><br />
\mathrm{sen}<br />
\left(<br />
\, \alpha \, + \beta \,<br />
\right)<br />
\, = \, \mathrm{sen}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{cos}<br />
\left(<br />
\, \beta \, <br />
\right) <br />
\, + \, <br />
\mathrm{cos}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{sen}<br />
\left(<br />
\, \beta \, <br />
\right)<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
Si en la formula anterior sustituimos &nbsp;<br />
<math><br />
\beta<br />
</math><br />
&nbsp; por &nbsp;<br />
<math><br />
-\beta<br />
</math><br />
&nbsp; obtenemos:<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{sen}<br />
\left(<br />
\, \alpha \, - \beta \,<br />
\right)<br />
\, = \, \mathrm{sen}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{cos}<br />
\left(<br />
\, -\beta \, <br />
\right) <br />
\, + \, <br />
\mathrm{cos}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{sen}<br />
\left(<br />
\, -\beta \, <br />
\right)<br />
\, = \, \, \mathrm{sen}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{cos}<br />
\left(<br />
\, \beta \, <br />
\right) <br />
\, - \, <br />
\mathrm{cos}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{sen}<br />
\left(<br />
\, \beta \, <br />
\right)<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{cos}<br />
\left(<br />
\, \alpha \, + \beta \,<br />
\right)<br />
\, = \, \mathrm{cos}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{cos}<br />
\left(<br />
\, \beta \, <br />
\right) <br />
\, - \, <br />
\mathrm{sen}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{sen}<br />
\left(<br />
\, \beta \, <br />
\right)<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
Si en la formula anterior sustituimos &nbsp;<br />
<math><br />
\beta<br />
</math><br />
&nbsp; por &nbsp;<br />
<math><br />
-\beta<br />
</math><br />
&nbsp; obtenemos:<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\mathrm{cos}<br />
\left(<br />
\, \alpha \, - \beta \,<br />
\right)<br />
\, = \, \mathrm{cos}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{cos}<br />
\left(<br />
\, -\beta \, <br />
\right) <br />
\, - \, <br />
\mathrm{sen}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{sen}<br />
\left(<br />
\, -\beta \, <br />
\right)<br />
\, = \, \, \mathrm{cos}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{cos}<br />
\left(<br />
\, \beta \, <br />
\right) <br />
\, + \, <br />
\mathrm{sen}<br />
\left(<br />
\, \alpha \, <br />
\right) <br />
\cdot \mathrm{sen}<br />
\left(<br />
\, \beta \, <br />
\right)<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
[[Category:Matemáticas]]</div>
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