http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?action=history&feed=atom&title=L%C3%B6sung_4.3%3A8d 2026-05-02T22:53:00Z Versionsgeschichte für diese Seite in Online Mathematik Brückenkurs 1 MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_4.3:8d&diff=8711&oldid=prev 2009-04-05T13:22:10Z

<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;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 13:22, 5. Apr. 2009</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</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;">It seems natural to try to use the addition formula on the numerator of the left-hand side,</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;">Wir verwenden das Additionstheorem und erhalten direkt</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>{{Abgesetzte Formel||&lt;math&gt;\begin{align}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Abgesetzte Formel||&lt;math&gt;\begin{align}</div></td></tr> </table>

Martin http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_4.3:8d&diff=7735&oldid=prev 2008-10-22T15:09:24Z

<p>hat „<a href="/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=Solution_4.3:8d&amp;action=edit" class="new" title="Solution 4.3:8d">Solution 4.3:8d</a>“ nach „<a href="/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.3:8d" title="Lösung 4.3:8d">Lösung 4.3:8d</a>“ verschoben: Robot: moved page</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;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 15:09, 22. Okt. 2008</td> </tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_4.3:8d&diff=6763&oldid=prev 2008-10-22T08:57:28Z

<p>Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)</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;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 08:57, 22. Okt. 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>It seems natural to try to use the addition formula on the numerator of the left-hand side,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>It seems natural to try to use the addition formula on the numerator of the left-hand side,</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>{{<del style="color: red; font-weight: bold; text-decoration: none;">Displayed math</del>||&lt;math&gt;\begin{align}</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;">Abgesetzte Formel</ins>||&lt;math&gt;\begin{align}</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\frac{\cos (u+v)}{\cos u\cos v}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\frac{\cos (u+v)}{\cos u\cos v}</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&amp;= \frac{\cos u\cdot\cos v - \sin u\cdot\sin v}{\cos u\cdot\cos v}\\[5pt] </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&amp;= \frac{\cos u\cdot\cos v - \sin u\cdot\sin v}{\cos u\cdot\cos v}\\[5pt] </div></td></tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_4.3:8d&diff=5860&oldid=prev 2008-10-10T08:40:41Z

<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;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 08:40, 10. Okt. 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>It seems natural to try to use the addition formula on the numerator of the left-hand side<del style="color: red; font-weight: bold; text-decoration: none;">:</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>It seems natural to try to use the addition formula on the numerator of the left-hand side<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;"></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>&#160;</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;">{{Displayed math||</ins>&lt;math&gt;\begin{align}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\begin{align}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\frac{\cos (u+v)}{\cos u\cos v}</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;">&amp; </del>\frac{\cos <del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( u+v <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)}{\cos u\cos v}=\frac{\cos u\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\cos v-\sin u\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\sin v}{\cos u\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\cos v} \\ </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;">&amp;</ins>= \frac{\cos u\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\cos v - \sin u\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\sin v}{\cos u\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\cos v}\\<ins style="color: red; font-weight: bold; text-decoration: none;">[5pt] </ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&amp; =1-\frac{\sin u\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\sin v}{\cos u\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\cos v}=1-\tan u\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\tan v<del style="color: red; font-weight: bold; text-decoration: none;">. </del>\\ </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&amp;= 1-\frac{\sin u\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\sin v}{\cos u\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\cos v}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[5pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\end{align}&lt;/math&gt;</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;">&amp;</ins>= 1-\tan u\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\tan v\<ins style="color: red; font-weight: bold; text-decoration: none;">,</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">textrm{.}</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\end{align}&lt;/math&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">}}</ins></div></td></tr> </table>

Tek http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_4.3:8d&diff=5679&oldid=prev 2008-09-30T11:13:30Z

<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;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 11:13, 30. Sep. 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</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;">NAVCONTENT_START</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;">It seems natural to try to use the addition formula on the numerator of the left-hand side:</ins></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;">&lt;center&gt; [[Image:4_3_8d</del>.<del style="color: red; font-weight: bold; text-decoration: none;">gif]] &lt;/center&gt;</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</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;">{NAVCONTENT_STOP}</del>}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</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;">&lt;math&gt;\begin</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">align}</ins></div></td></tr> <tr><td colspan="2">&nbsp;</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;">&amp; \frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">\cos \left( u+v \right)</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">{\cos u\cos v}=\frac{\cos u\centerdot \cos v-\sin u\centerdot \sin v}{\cos u\centerdot \cos v</ins>} <ins style="color: red; font-weight: bold; text-decoration: none;">\\ </ins></div></td></tr> <tr><td colspan="2">&nbsp;</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;">&amp; =1-\frac{\sin u\centerdot \sin v}{\cos u\centerdot \cos v}=1-\tan u\centerdot \tan v</ins>. <ins style="color: red; font-weight: bold; text-decoration: none;">\\ </ins></div></td></tr> <tr><td colspan="2">&nbsp;</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;">\end</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">align</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins></div></td></tr> </table>

Ian http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_4.3:8d&diff=3900&oldid=prev 2008-09-09T09:59:03Z

<p><a href="/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sning_4.3:8d&amp;action=edit" class="new" title="Lösning 4.3:8d">Lösning 4.3:8d</a> moved to <a href="/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=Solution_4.3:8d&amp;action=edit" class="new" title="Solution 4.3:8d">Solution 4.3:8d</a>: Robot: moved page</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;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 09:59, 9. Sep. 2008</td> </tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_4.3:8d&diff=2466&oldid=prev 2008-08-21T07:16:39Z

<p>Robot: Automated text replacement (-[[Bild: +[[Image:)</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;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 07:16, 21. Aug. 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;center&gt; [[<del style="color: red; font-weight: bold; text-decoration: none;">Bild</del>:4_3_8d.gif]] &lt;/center&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;center&gt; [[<ins style="color: red; font-weight: bold; text-decoration: none;">Image</ins>:4_3_8d.gif]] &lt;/center&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td></tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_4.3:8d&diff=1374&oldid=prev 2008-04-03T10:56:38Z

<p>Ny sida: {{NAVCONTENT_START}} &lt;center&gt; <a href="/wikis/2009/bridgecourse1-TU-Berlin/index.php/Bild:4_3_8d.gif" title="Bild:4 3 8d.gif">Bild:4_3_8d.gif</a> &lt;/center&gt; {{NAVCONTENT_STOP}}</p> <p><b>Neue Seite</b></p><div>{{NAVCONTENT_START}}<br /> &lt;center&gt; [[Bild:4_3_8d.gif]] &lt;/center&gt;<br /> {{NAVCONTENT_STOP}}</div>

Oskar