http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?action=history&feed=atom&title=Solution_4.3%3A3b 2026-04-08T07:35:59Z Revision history for this page on the wiki MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_4.3:3b&diff=5837&oldid=prev 2008-10-09T13:23:11Z

<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;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 13:23, 9 October 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The angle </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The angle &lt;math&gt;\pi-v&lt;/math&gt; makes the same angle with the negative <ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>x<ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>-axis as the angle &lt;math&gt;v&lt;/math&gt; makes with the positive <ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>x<ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>-axis and this means that &lt;math&gt;\pi-v&lt;/math&gt; is the reflection of &lt;math&gt;v&lt;/math&gt; in the <ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>y<ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>-axis.</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\pi -v<del style="color: red; font-weight: bold; text-decoration: none;">\text{ }</del>&lt;/math&gt;</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: #ffa; color:black; font-size: smaller;"><div>makes the same angle with the negative </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: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;</del>x<del style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</del></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: #ffa; color:black; font-size: smaller;"><div>-axis as the angle </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: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;v&lt;/math&gt;</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: #ffa; color:black; font-size: smaller;"><div>makes with the positive </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: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;</del>x<del style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</del></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: #ffa; color:black; font-size: smaller;"><div>-axis and this means that </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: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\pi -v<del style="color: red; font-weight: bold; text-decoration: none;">\text{ }</del>&lt;/math&gt;</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: #ffa; color:black; font-size: smaller;"><div>is the reflection of </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: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;v&lt;/math&gt;</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: #ffa; color:black; font-size: smaller;"><div>in the y-axis.</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>[[Image:4_3_3_b.gif|center]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:4_3_3_b.gif|center]]</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>Under such reflection, the angle's </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Under such reflection, the angle's <ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>y<ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>-coordinate does not change (but the <ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>x<ins style="color: red; font-weight: bold; text-decoration: none;">''</ins>-coordinate changes sign) and therefore &lt;math&gt;\sin (\pi-v) = \sin v = a<ins style="color: red; font-weight: bold; text-decoration: none;">\,</ins>&lt;/math&gt;.</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;math&gt;</del>y<del style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</del></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: #ffa; color:black; font-size: smaller;"><div>-coordinate does not change (but the </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: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;</del>x<del style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</del></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: #ffa; color:black; font-size: smaller;"><div>-coordinate changes sign) and therefore </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: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\<del style="color: red; font-weight: bold; text-decoration: none;">text{</del>sin<del style="color: red; font-weight: bold; text-decoration: none;">}\left</del>( \pi -v <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)=\<del style="color: red; font-weight: bold; text-decoration: none;">text{</del>sin <del style="color: red; font-weight: bold; text-decoration: none;">}</del>v<del style="color: red; font-weight: bold; text-decoration: none;">\text{ }</del>=a&lt;/math&gt;.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> </table>

Tek http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_4.3:3b&diff=5606&oldid=prev 2008-09-29T10:51:07Z

<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;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 10:51, 29 September 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 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;">The angle </ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;<del style="color: red; font-weight: bold; text-decoration: none;">center</del>&gt; <del style="color: red; font-weight: bold; text-decoration: none;">[[Image:4_3_3b.gif]] </del>&lt;/<del style="color: red; font-weight: bold; text-decoration: none;">center</del>&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;">&lt;math&gt;\pi -v\text</ins>{ }<ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</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;">{NAVCONTENT_STOP}</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;">makes the same angle with the negative </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>&lt;<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">x</ins>&lt;/<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;</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;">-axis as the angle </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;">&lt;math&gt;v&lt;/math&gt;</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;">makes with the positive </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;">&lt;math&gt;x&lt;/math&gt;</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;">-axis and this means that </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;">&lt;math&gt;\pi -v\text</ins>{ }<ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</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;">is the reflection of </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;">&lt;math&gt;v&lt;/math&gt;</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;">in the y-axis.</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>&#160;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:4_3_3_b.gif|center]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Image:4_3_3_b.gif|center]]</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Under such reflection, the angle's </div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;math&gt;y&lt;/math&gt;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>-coordinate does not change (but the </div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;math&gt;x&lt;/math&gt;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>-coordinate changes sign) and therefore </div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;math&gt;\text{sin}\left( \pi -v \right)=\text{sin }v\text{ }=a&lt;/math&gt;.</div></td></tr> </table>

Ian http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_4.3:3b&diff=3840&oldid=prev 2008-09-09T09:52:23Z

<p><a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=L%C3%B6sning_4.3:3b&amp;action=edit" class="new" title="Lösning 4.3:3b">Lösning 4.3:3b</a> moved to <a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php/Solution_4.3:3b" title="Solution 4.3:3b">Solution 4.3:3b</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;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 09:52, 9 September 2008</td> </tr> </table>

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<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;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 14:15, 18 August 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;center&gt; [[Bild:4_3_3b.gif]] &lt;/center&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;center&gt; [[Bild:4_3_3b.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> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Bild:4_3_3_b.gif|center]]</div></td></tr> </table>

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