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Övningar 4.2 - Versionshistorik
2026-04-24T21:01:42Z
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KTH.SE:u1zpa8nw den 17 juli 2007 kl. 10.56
2007-07-17T10:56:41Z
<p></p>
<table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;">
<tr>
<td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 17 juli 2007 kl. 10.56</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 51:</strong></td>
<td colspan="2" align="left"><strong>Rad 51:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></table></td><td> </td><td style="background: #eee; font-size: smaller;"></table></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 4.2:3'''</td><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 4.2:3'''</td></tr>
</table>
KTH.SE:u1zpa8nw
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KTH.SE:u1zpa8nw den 17 juli 2007 kl. 09.45
2007-07-17T09:45:26Z
<p></p>
<table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;">
<tr>
<td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 17 juli 2007 kl. 09.45</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 161:</strong></td>
<td colspan="2" align="left"><strong>Rad 161:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></table></td><td> </td><td style="background: #eee; font-size: smaller;"></table></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br></td></tr>
</table>
KTH.SE:u1zpa8nw
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KTH.SE:u1zpa8nw den 16 juli 2007 kl. 11.39
2007-07-16T11:39:00Z
<p></p>
<table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;">
<tr>
<td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 16 juli 2007 kl. 11.39</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 1:</strong></td>
<td colspan="2" align="left"><strong>Rad 1:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">__NOTOC__</td><td> </td><td style="background: #eee; font-size: smaller;">__NOTOC__</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 4.2:1'''</td><td> </td><td style="background: #eee; font-size: smaller;">'''Övning 4.2:1'''</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Bestäm längden av sidan som är markerad med $\,x\,$ uttryckt med hjälp av de trigonometriska funktionerna.</td><td> </td><td style="background: #eee; font-size: smaller;">Bestäm längden av sidan som är markerad med $\,x\,$ uttryckt med hjälp av de trigonometriska funktionerna.</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><table width="100%"></td><td> </td><td style="background: #eee; font-size: smaller;"><table width="100%"></td></tr>
</table>
KTH.SE:u1zpa8nw
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KTH.SE:u1zpa8nw den 16 juli 2007 kl. 11.38
2007-07-16T11:38:22Z
<p></p>
<table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;">
<tr>
<td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 16 juli 2007 kl. 11.38</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 1:</strong></td>
<td colspan="2" align="left"><strong>Rad 1:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">__NOTOC__</td><td> </td><td style="background: #eee; font-size: smaller;">__NOTOC__</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:1<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:1<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><div class="ovning"></td><td> </td><td style="background: #eee; font-size: smaller;"><div class="ovning"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Bestäm längden av sidan som är markerad med $\,x\,$ uttryckt med hjälp av de trigonometriska funktionerna.</td><td> </td><td style="background: #eee; font-size: smaller;">Bestäm längden av sidan som är markerad med $\,x\,$ uttryckt med hjälp av de trigonometriska funktionerna.</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">a)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">a)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1a.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1a.gif]]</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">b)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">b)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1b.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1b.gif]]</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">c)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">c)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1c.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1c.gif]]</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">d)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">d)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1d.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1d.gif]]</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">e)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">e)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1e.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1e.gif]]</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">f)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">f)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1f.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_1f.gif]]</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 26:</strong></td>
<td colspan="2" align="left"><strong>Rad 26:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:2<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:2<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Bestäm en trigonometrisk ekvation som vinkeln $\,v\,$ uppfyller.</td><td> </td><td style="background: #eee; font-size: smaller;">Bestäm en trigonometrisk ekvation som vinkeln $\,v\,$ uppfyller.</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">a)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">a)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2a.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2a.gif]]</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">b)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">b)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2b.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2b.gif]]</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">c)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">c)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2c.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2c.gif]]</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">d)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">d)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2d.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2d.gif]]</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left" valign="top"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">e)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">e)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2e.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2e.gif]]</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">f)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">f)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2f.gif]]</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">[[Bild:O4_2_2f.gif]]</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 52:</strong></td>
<td colspan="2" align="left"><strong>Rad 52:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:3<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:3<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Bestäm</td><td> </td><td style="background: #eee; font-size: smaller;">Bestäm</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">a)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">a)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%"> $\sin{\left(-\displaystyle \frac{\pi}{2}\right)}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%"> $\sin{\left(-\displaystyle \frac{\pi}{2}\right)}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">b)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">b)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{2\pi}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{2\pi}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">c)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">c)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{9\pi}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{9\pi}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">d)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">d)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%"> $\cos{\displaystyle \frac{7\pi}{2}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%"> $\cos{\displaystyle \frac{7\pi}{2}}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">e)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">e)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{\displaystyle \frac{3\pi}{4}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{\displaystyle \frac{3\pi}{4}}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">f)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">f)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{\left(-\displaystyle \frac{\pi}{6}\right)}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{\left(-\displaystyle \frac{\pi}{6}\right)}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 76:</strong></td>
<td colspan="2" align="left"><strong>Rad 76:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:4<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:4<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Bestäm</td><td> </td><td style="background: #eee; font-size: smaller;">Bestäm</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">a)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">a)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{\displaystyle \frac{11\pi}{6}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{\displaystyle \frac{11\pi}{6}}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">b)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">b)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{\displaystyle \frac{11\pi}{3}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{\displaystyle \frac{11\pi}{3}}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">c)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">c)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\tan{\displaystyle \frac{3\pi}{4}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\tan{\displaystyle \frac{3\pi}{4}}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">d)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">d)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\tan{\pi}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\tan{\pi}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">e)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">e)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\tan{\displaystyle \frac{7\pi}{6}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\tan{\displaystyle \frac{7\pi}{6}}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">f)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">f)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\tan{\left(-\displaystyle \frac{5\pi}{3}\right)}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\tan{\left(-\displaystyle \frac{5\pi}{3}\right)}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 100:</strong></td>
<td colspan="2" align="left"><strong>Rad 100:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:5<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:5<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Bestäm</td><td> </td><td style="background: #eee; font-size: smaller;">Bestäm</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">a)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">a)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="25%">$\cos{135^\circ}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="25%">$\cos{135^\circ}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">b)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">b)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="25%">$\tan{225^\circ}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="25%">$\tan{225^\circ}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">c)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">c)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="25%">$\cos{330^\circ}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="25%">$\cos{330^\circ}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">d)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">d)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="25%">$\tan{495^\circ}$</td> </td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="25%">$\tan{495^\circ}$</td> </td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 118:</strong></td>
<td colspan="2" align="left"><strong>Rad 118:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:6<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:6<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Bestäm längden av sidan som är markerad med $\,x\,$.</td><td> </td><td style="background: #eee; font-size: smaller;">Bestäm längden av sidan som är markerad med $\,x\,$.</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="center"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="100%">[[Bild:O4_2_6.gif]]</td> </td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="100%">[[Bild:O4_2_6.gif]]</td> </td></tr>
<tr><td colspan="2" align="left"><strong>Rad 129:</strong></td>
<td colspan="2" align="left"><strong>Rad 129:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:7<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:7<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">För att mäta upp bredden av en älv mäter vi från två punkter A och B längs den ena raka stranden vinkeln till ett träd C på motsatt sida älven. Hur bred är älven om måtten i figuren gäller?</td><td> </td><td style="background: #eee; font-size: smaller;">För att mäta upp bredden av en älv mäter vi från två punkter A och B längs den ena raka stranden vinkeln till ett träd C på motsatt sida älven. Hur bred är älven om måtten i figuren gäller?</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="center"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="100%">[[Bild:O_4_2_7.gif]]</td> </td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="100%">[[Bild:O_4_2_7.gif]]</td> </td></tr>
<tr><td colspan="2" align="left"><strong>Rad 140:</strong></td>
<td colspan="2" align="left"><strong>Rad 140:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:8<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:8<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">En stång med längd $\,\ell\,$ är upphängd i två linor med längd $\,a\,$ resp. $\,b\,$ enligt figuren. Linorna bildar vinklar $\,\alpha\,$ resp. $\,\beta\,$ med vertikalen. Bestäm en trigonometrisk ekvation för vinkeln $\,\gamma\,$ som stången bildar med vertikalen.</td><td> </td><td style="background: #eee; font-size: smaller;">En stång med längd $\,\ell\,$ är upphängd i två linor med längd $\,a\,$ resp. $\,b\,$ enligt figuren. Linorna bildar vinklar $\,\alpha\,$ resp. $\,\beta\,$ med vertikalen. Bestäm en trigonometrisk ekvation för vinkeln $\,\gamma\,$ som stången bildar med vertikalen.</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="center"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="100%">[[Bild:O_4_2_8.gif]]</td> </td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="100%">[[Bild:O_4_2_8.gif]]</td> </td></tr>
<tr><td colspan="2" align="left"><strong>Rad 151:</strong></td>
<td colspan="2" align="left"><strong>Rad 151:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">==</span>Övning 4.2:9<span style="color: red; font-weight: bold;">==</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">'''</span>Övning 4.2:9<span style="color: red; font-weight: bold;">'''</span></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><div class="ovning"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><div class="ovning<span style="color: red; font-weight: bold;">" style="margin-top:-20px; margin-bottom:-5px;</span>"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">Bilvägen från ''A'' till ''B'' består av tre rätlinjiga delar ''AP'', ''PQ'' och ''QB'', vilka är 4,0 km, 12,0 km respektive 5,0 km. De i figuren markerade vinklarna vid ''P'' och ''Q'' är 30° respektive 90°. Beräkna avståndet fågelvägen från ''A'' till ''B''. (Uppgiften är hämtad ur Centrala provet i matematik, november 1976, men aningen modifierad.)</td><td> </td><td style="background: #eee; font-size: smaller;">Bilvägen från ''A'' till ''B'' består av tre rätlinjiga delar ''AP'', ''PQ'' och ''QB'', vilka är 4,0 km, 12,0 km respektive 5,0 km. De i figuren markerade vinklarna vid ''P'' och ''Q'' är 30° respektive 90°. Beräkna avståndet fågelvägen från ''A'' till ''B''. (Uppgiften är hämtad ur Centrala provet i matematik, november 1976, men aningen modifierad.)</td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><table width="100%<span style="color: red; font-weight: bold;">" cellspacing="10px</span>"></td><td>+</td><td style="background: #cfc; font-size: smaller;"><table width="100%"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="center"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="100%">[[Bild:O4_2_9.gif]]</td> </td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="100%">[[Bild:O4_2_9.gif]]</td> </td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vningar_4.2&diff=2253&oldid=prev
KTH.SE:u1zpa8nw: Ny sida: __NOTOC__ ==Övning 4.2:1== <div class="ovning"> Bestäm längden av sidan som är markerad med $\,x\,$ uttryckt med hjälp av de trigonometriska funktionerna. <table width="100%" cellspaci...
2007-07-16T08:16:15Z
<p>Ny sida: __NOTOC__ ==Övning 4.2:1== <div class="ovning"> Bestäm längden av sidan som är markerad med $\,x\,$ uttryckt med hjälp av de trigonometriska funktionerna. <table width="100%" cellspaci...</p>
<p><b>Ny sida</b></p><div>__NOTOC__<br />
==Övning 4.2:1==<br />
<div class="ovning"><br />
Bestäm längden av sidan som är markerad med $\,x\,$ uttryckt med hjälp av de trigonometriska funktionerna.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left" valign="top"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_1a.gif]]</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_1b.gif]]</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_1c.gif]]</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_1d.gif]]</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_1e.gif]]</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_1f.gif]]</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 4.2:2==<br />
<div class="ovning"><br />
Bestäm en trigonometrisk ekvation som vinkeln $\,v\,$ uppfyller.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left" valign="top"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_2a.gif]]</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_2b.gif]]</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_2c.gif]]</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_2d.gif]]</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_2e.gif]]</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="50%">[[Bild:O4_2_2f.gif]]</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 4.2:3==<br />
<div class="ovning"><br />
Bestäm<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%"> $\sin{\left(-\displaystyle \frac{\pi}{2}\right)}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\cos{2\pi}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\sin{9\pi}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%"> $\cos{\displaystyle \frac{7\pi}{2}}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$\sin{\displaystyle \frac{3\pi}{4}}$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$\cos{\left(-\displaystyle \frac{\pi}{6}\right)}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 4.2:4==<br />
<div class="ovning"><br />
Bestäm<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\cos{\displaystyle \frac{11\pi}{6}}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\cos{\displaystyle \frac{11\pi}{3}}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\tan{\displaystyle \frac{3\pi}{4}}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$\tan{\pi}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$\tan{\displaystyle \frac{7\pi}{6}}$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$\tan{\left(-\displaystyle \frac{5\pi}{3}\right)}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 4.2:5==<br />
<div class="ovning"><br />
Bestäm<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$\cos{135^\circ}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$\tan{225^\circ}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$\cos{330^\circ}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$\tan{495^\circ}$</td> <br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 4.2:6==<br />
<div class="ovning"><br />
Bestäm längden av sidan som är markerad med $\,x\,$.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="center"><br />
<td class="ntext" width="100%">[[Bild:O4_2_6.gif]]</td> <br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 4.2:7==<br />
<div class="ovning"><br />
För att mäta upp bredden av en älv mäter vi från två punkter A och B längs den ena raka stranden vinkeln till ett träd C på motsatt sida älven. Hur bred är älven om måtten i figuren gäller?<br />
<table width="100%" cellspacing="10px"><br />
<tr align="center"><br />
<td class="ntext" width="100%">[[Bild:O_4_2_7.gif]]</td> <br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 4.2:8==<br />
<div class="ovning"><br />
En stång med längd $\,\ell\,$ är upphängd i två linor med längd $\,a\,$ resp. $\,b\,$ enligt figuren. Linorna bildar vinklar $\,\alpha\,$ resp. $\,\beta\,$ med vertikalen. Bestäm en trigonometrisk ekvation för vinkeln $\,\gamma\,$ som stången bildar med vertikalen.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="center"><br />
<td class="ntext" width="100%">[[Bild:O_4_2_8.gif]]</td> <br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 4.2:9==<br />
<div class="ovning"><br />
Bilvägen från ''A'' till ''B'' består av tre rätlinjiga delar ''AP'', ''PQ'' och ''QB'', vilka är 4,0 km, 12,0 km respektive 5,0 km. De i figuren markerade vinklarna vid ''P'' och ''Q'' är 30° respektive 90°. Beräkna avståndet fågelvägen från ''A'' till ''B''. (Uppgiften är hämtad ur Centrala provet i matematik, november 1976, men aningen modifierad.)<br />
<table width="100%" cellspacing="10px"><br />
<tr align="center"><br />
<td class="ntext" width="100%">[[Bild:O4_2_9.gif]]</td> <br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div></div>
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