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Övningar 4.4 - Versionshistorik
2026-05-16T17:26:43Z
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KTH.SE:u1zpa8nw den 17 juli 2007 kl. 09.46
2007-07-17T09:46:44Z
<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. 09.46</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 150:</strong></td>
<td colspan="2" align="left"><strong>Rad 150:</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><br><br><br><br><br><br><br><br><br><br><br><br></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></td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vningar_4.4&diff=2304&oldid=prev
KTH.SE:u1zpa8nw den 16 juli 2007 kl. 11.44
2007-07-16T11:44:56Z
<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. 11.44</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>&Ouml;vning 4.4:1<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>&Ouml;vning 4.4:1<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 vilka vinklar $\,v\,$, där $\,0 \leq v\leq 2\pi\,$, gäller att</td><td> </td><td style="background: #eee; font-size: smaller;">För vilka vinklar $\,v\,$, där $\,0 \leq v\leq 2\pi\,$, gäller att</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="50%">$\sin{v}=\displaystyle \frac{1}{2}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{v}=\displaystyle \frac{1}{2}$</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%">$\cos{v}=\displaystyle \frac{1}{2}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\cos{v}=\displaystyle \frac{1}{2}$</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">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%">$\sin{v}=1$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{v}=1$</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%">$\tan{v}=1$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\tan{v}=1$</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">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%">$\cos{v}=2$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\cos{v}=2$</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%">$\sin{v}=-\displaystyle \frac{1}{2}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{v}=-\displaystyle \frac{1}{2}$</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">g)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">g)<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%">$\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}$</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 30:</strong></td>
<td colspan="2" align="left"><strong>Rad 30:</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>&Ouml;vning 4.4:2<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>&Ouml;vning 4.4:2<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;">L&ouml;s ekvationen</td><td> </td><td style="background: #eee; font-size: smaller;">L&ouml;s ekvationen</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%">$\sin{x}=\displaystyle \frac{\sqrt{3}}{2}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{x}=\displaystyle \frac{\sqrt{3}}{2}$</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{x}=\displaystyle \frac{1}{2} $</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{x}=\displaystyle \frac{1}{2} $</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">c)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">c)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{x}=0$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{x}=0$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">d)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">d)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{5x}=\displaystyle \frac{1}{\sqrt{2}} $</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{5x}=\displaystyle \frac{1}{\sqrt{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{5x}=\displaystyle \frac{1}{2}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\sin{5x}=\displaystyle \frac{1}{2}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">f)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">f)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}$</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 54:</strong></td>
<td colspan="2" align="left"><strong>Rad 54:</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>&Ouml;vning 4.4:3<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>&Ouml;vning 4.4:3<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;">Lös ekvationen</td><td> </td><td style="background: #eee; font-size: smaller;">Lös ekvationen</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="50%">$\cos{x}=\cos{\displaystyle \frac{\pi}{6}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\cos{x}=\cos{\displaystyle \frac{\pi}{6}}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">b)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">b)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{x}=\sin{\displaystyle \frac{\pi}{5}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{x}=\sin{\displaystyle \frac{\pi}{5}}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">c)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">c)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="50%">$\sin{(x+40^\circ)}=\sin{65^\circ}$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="50%">$\sin{(x+40^\circ)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span>}=\sin{65^\circ}$</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext">d)</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext">d)<span style="color: red; font-weight: bold;">&nbsp;&nbsp;&nbsp;</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{3x}=\sin{15^\circ}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{3x}=\sin{15^\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 74:</strong></td>
<td colspan="2" align="left"><strong>Rad 74:</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>&Ouml;vning 4.4:4<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>&Ouml;vning 4.4:4<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 de vinklar $\,v\,$ i intervallet $\,0^\circ \leq v \leq 360^\circ\,$ som uppfyller $\ \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}\,$.</td><td> </td><td style="background: #eee; font-size: smaller;">Bestäm de vinklar $\,v\,$ i intervallet $\,0^\circ \leq v \leq 360^\circ\,$ som uppfyller $\ \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}\,$.</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>&Ouml;vning 4.4:5<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>&Ouml;vning 4.4:5<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;">Lös ekvationen</td><td> </td><td style="background: #eee; font-size: smaller;">Lös ekvationen</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="50%">$\sin{3x}=\sin{x}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{3x}=\sin{x}$</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%">$\tan{x}=\tan{4x}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\tan{x}=\tan{4x}$</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">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%">$\cos{5x}=\cos(x+\pi/5)$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\cos{5x}=\cos(x+\pi/5)$</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 97:</strong></td>
<td colspan="2" align="left"><strong>Rad 97:</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>&Ouml;vning 4.4:6<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>&Ouml;vning 4.4:6<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;">Lös ekvationen</td><td> </td><td style="background: #eee; font-size: smaller;">Lös ekvationen</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="50%">$\sin x\cdot \cos 3x = 2\sin x$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin x\cdot \cos 3x = 2\sin x$</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%">$\sqrt{2}\sin{x}\cos{x}=\cos{x}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sqrt{2}\sin{x}\cos{x}=\cos{x}$</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">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%">$\sin 2x = -\sin x$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin 2x = -\sin x$</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 115:</strong></td>
<td colspan="2" align="left"><strong>Rad 115:</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>&Ouml;vning 4.4:7<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>&Ouml;vning 4.4:7<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;">Lös ekvationen</td><td> </td><td style="background: #eee; font-size: smaller;">Lös ekvationen</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="50%">$2\sin^2{x}+\sin{x}=1$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$2\sin^2{x}+\sin{x}=1$</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%">$2\sin^2{x}-3\cos{x}=0$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$2\sin^2{x}-3\cos{x}=0$</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">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%">$\cos{3x}=\sin{4x}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\cos{3x}=\sin{4x}$</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 133:</strong></td>
<td colspan="2" align="left"><strong>Rad 133:</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>&Ouml;vning 4.4:8<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>&Ouml;vning 4.4:8<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;">Lös ekvationen</td><td> </td><td style="background: #eee; font-size: smaller;">Lös ekvationen</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="50%">$\sin{2x}=\sqrt{2}\cos{x}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{2x}=\sqrt{2}\cos{x}$</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%">$\sin{x}=\sqrt{3}\cos{x}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\sin{x}=\sqrt{3}\cos{x}$</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">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%">$\displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="50%">$\displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}$</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>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vningar_4.4&diff=2255&oldid=prev
KTH.SE:u1zpa8nw: Ny sida: __NOTOC__ ==Övning 4.4:1== <div class="ovning"> För vilka vinklar $\,v\,$, där $\,0 \leq v\leq 2\pi\,$, gäller att <table width="100%" cellspacing="10px"> <tr align="left"> <td clas...
2007-07-16T08:17:40Z
<p>Ny sida: __NOTOC__ ==&Ouml;vning 4.4:1== <div class="ovning"> För vilka vinklar $\,v\,$, där $\,0 \leq v\leq 2\pi\,$, gäller att <table width="100%" cellspacing="10px"> <tr align="left"> <td clas...</p>
<p><b>Ny sida</b></p><div>__NOTOC__<br />
==&Ouml;vning 4.4:1==<br />
<div class="ovning"><br />
För vilka vinklar $\,v\,$, där $\,0 \leq v\leq 2\pi\,$, gäller att<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\sin{v}=\displaystyle \frac{1}{2}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\cos{v}=\displaystyle \frac{1}{2}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\sin{v}=1$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\tan{v}=1$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="50%">$\cos{v}=2$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="50%">$\sin{v}=-\displaystyle \frac{1}{2}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">g)</td><br />
<td class="ntext" width="50%">$\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 4.4:2==<br />
<div class="ovning"><br />
L&ouml;s ekvationen<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\sin{x}=\displaystyle \frac{\sqrt{3}}{2}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\cos{x}=\displaystyle \frac{1}{2} $</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\sin{x}=0$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$\sin{5x}=\displaystyle \frac{1}{\sqrt{2}} $</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$\sin{5x}=\displaystyle \frac{1}{2}$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 4.4:3==<br />
<div class="ovning"><br />
Lös ekvationen<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\cos{x}=\cos{\displaystyle \frac{\pi}{6}}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\sin{x}=\sin{\displaystyle \frac{\pi}{5}}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\sin{(x+40^\circ)}=\sin{65^\circ}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\sin{3x}=\sin{15^\circ}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 4.4:4==<br />
<div class="ovning"><br />
Bestäm de vinklar $\,v\,$ i intervallet $\,0^\circ \leq v \leq 360^\circ\,$ som uppfyller $\ \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}\,$.<br />
</div><br />
<br />
==&Ouml;vning 4.4:5==<br />
<div class="ovning"><br />
Lös ekvationen<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\sin{3x}=\sin{x}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\tan{x}=\tan{4x}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\cos{5x}=\cos(x+\pi/5)$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 4.4:6==<br />
<div class="ovning"><br />
Lös ekvationen<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\sin x\cdot \cos 3x = 2\sin x$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\sqrt{2}\sin{x}\cos{x}=\cos{x}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\sin 2x = -\sin x$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 4.4:7==<br />
<div class="ovning"><br />
Lös ekvationen<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$2\sin^2{x}+\sin{x}=1$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$2\sin^2{x}-3\cos{x}=0$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\cos{3x}=\sin{4x}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 4.4:8==<br />
<div class="ovning"><br />
Lös ekvationen<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\sin{2x}=\sqrt{2}\cos{x}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\sin{x}=\sqrt{3}\cos{x}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div></div>
KTH.SE:u1zpa8nw