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4.4 Övningar

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(Övning 4.4:7)
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Nuvarande version (31 maj 2007 kl. 07.05) (redigera) (ogör)
KTH.SE:u1rp004j (Diskussion | bidrag)

 
(9 mellanliggande versioner visas inte.)
Rad 1: Rad 1:
-==Övning 4.4:1==+ 
 +==Övning 4.4:1==
<div class="ovning"> <div class="ovning">
-För vilka vinklar v, där 0 \leq v\leq 2\pi, gäller att+För vilka vinklar $\,v\,, där \,0 \leq v\leq 2\pi\,$, gäller att
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">\sin{v}=\displaystyle \frac{1}{2}</td>+<td class="ntext" width="50%">\sin{v}=\displaystyle \frac{1}{2}</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$\cos{v}=\displaystyle \frac{1}{2}$</td>+<td class="ntext" width="50%">\cos{v}=\displaystyle \frac{1}{2}</td>
-<td class="ntext">\textrm{c) }</td>+
-<td class="ntext">$\sin{v}=1$</td>+
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">\tan{v}=1</td>+<td class="ntext" width="50%">$\sin{v}=1$</td>
-<td class="ntext">$\textrm{e) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">\cos{v}=2</td>+<td class="ntext" width="50%">\tan{v}=1</td>
-<td class="ntext">$\textrm{f) }$</td>+</tr>
-<td class="ntext">\sin{v}=-\displaystyle \frac{1}{2}</td>+<tr align="left">
 +<td class="ntext">e)</td>
 +<td class="ntext" width="50%">\cos{v}=2</td>
 +<td class="ntext">f)</td>
 +<td class="ntext" width="50%">\sin{v}=-\displaystyle \frac{1}{2}</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{g) }$</td>+<td class="ntext">g)</td>
-<td class="ntext">\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}</td>+<td class="ntext" width="50%">\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}</td>
-<td class="ntext"></td>+
-<td class="ntext"></td>+
-<td class="ntext"></td>+
-<td class="ntext"></td>+
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 36: Rad 33:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">\displaystyle v=\frac{\pi}{6}, \displaystyle v=\frac{5\pi}{6}</td>+<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{6}\,, \,\displaystyle v=\frac{5\pi}{6}$</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$\displaystyle v=\frac{\pi}{3}, \displaystyle v=\frac{5\pi}{3}$</td>+<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{3}\,$, $\,\displaystyle v=\frac{5\pi}{3}$</td>
-<td class="ntext">$\textrm{c) }$</td>+
-<td class="ntext">$\displaystyle v=\frac{\pi}{2}$</td>+
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">$\displaystyle v=\frac{\pi}{4},\displaystyle v=\frac{5\pi}{4}$</td>+<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{2}$</td>
-<td class="ntext">$\textrm{e) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">\textrm{lösning saknas}</td>+<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{4}\,, \,\displaystyle v=\frac{5\pi}{4}$</td>
-<td class="ntext">\textrm{f) }</td>+
-<td class="ntext">$\displaystyle v=\frac{11\pi}{6}, \displaystyle v=\frac{7\pi}{6}$</td>+
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{g) }$</td>+<td class="ntext">e)</td>
-<td class="ntext">$\displaystyle v=\frac{5\pi}{6}, \displaystyle v=\frac{11\pi}{6}$</td>+<td class="ntext" width="50%">lösning saknas</td>
-<td class="ntext"></td>+<td class="ntext">f)</td>
-<td class="ntext"></td>+<td class="ntext" width="50%">$\displaystyle v=\frac{11\pi}{6}\,, \,\displaystyle v=\frac{7\pi}{6}$</td>
-<td class="ntext"></td>+</tr>
-<td class="ntext"></td>+<tr align="left">
 +<td class="ntext">g)</td>
 +<td class="ntext" width="50%">\displaystyle v=\frac{5\pi}{6}\,, \,\displaystyle v=\frac{11\pi}{6}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 70: Rad 63:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br />[[Bild:4_4_1a.gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_1a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</DIV>+<div class=NavHead>L&ouml;sning b)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br />[[Bild:4_4_1b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_1b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br />[[Bild:4_4_1c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_1c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br />[[Bild:4_4_1d.gif]]+Lösning till delfråga d)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_1d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</DIV>+<div class=NavHead>L&ouml;sning e)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e<br />[[Bild:4_4_1e.gif]]+Lösning till delfråga e)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_1e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga f<br />[[Bild:4_4_1f.gif]]+Lösning till delfråga f)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_1f.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning g&nbsp;</div>+<div class=NavHead>L&ouml;sning g)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga g<br />[[Bild:4_4_1g-1(2).gif]]<br />[[Bild:4_4_1g-2(2).gif]]+Lösning till delfråga g)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_1g-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_1g-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
-==Övning 4.4:2==+==&Ouml;vning 4.4:2==
<div class="ovning"> <div class="ovning">
L&ouml;s ekvationen L&ouml;s ekvationen
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">\sin{x}=\displaystyle \frac{\sqrt{3}}{2}</td>+<td class="ntext" width="33%">\sin{x}=\displaystyle \frac{\sqrt{3}}{2}</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">\cos{x}=\displaystyle \frac{1}{2} </td>+<td class="ntext" width="33%">\cos{x}=\displaystyle \frac{1}{2} </td>
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">\sin{x}=0</td>+<td class="ntext" width="33%">\sin{x}=0</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">\sin{5x}=\displaystyle \frac{1}{\sqrt{2}} </td>+<td class="ntext" width="33%">\sin{5x}=\displaystyle \frac{1}{\sqrt{2}} </td>
-<td class="ntext">$\textrm{e) }$</td>+<td class="ntext">e)</td>
-<td class="ntext">\sin{5x}=\displaystyle \frac{1}{2}</td>+<td class="ntext" width="33%">\sin{5x}=\displaystyle \frac{1}{2}</td>
-<td class="ntext">$\textrm{f) }$</td>+<td class="ntext">f)</td>
-<td class="ntext">\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}</td>+<td class="ntext" width="33%">\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 147: Rad 192:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">+<td class="ntext" width="33%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=\displaystyle\frac{\pi}{3}+2n\pi\cr+x&=\displaystyle\frac{\pi}{3}+2n\pi\cr
-x=\displaystyle\frac{2\pi}{3}+2n\pi } \right.$+x&=\displaystyle\frac{2\pi}{3}+2n\pi } \right.$
</td> </td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">+<td class="ntext" width="33%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=\displaystyle\frac{\pi}{3}+2n\pi\cr+x&=\displaystyle\frac{\pi}{3}+2n\pi\cr
-x=\displaystyle\frac{5\pi}{3}+2n\pi } \right.$+x&=\displaystyle\frac{5\pi}{3}+2n\pi } \right.$
</td> </td>
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">+<td class="ntext" width="33%">
x=n\pi</td> x=n\pi</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">+<td class="ntext" width="33%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=\displaystyle\frac{\pi}{20}+\displaystyle\frac{2n\pi}{5}\cr+x&=\displaystyle\frac{\pi}{20}+\displaystyle\frac{2n\pi}{5}\cr
-x=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.$+x&=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.$
 +</td>
 +<td class="ntext">e)</td>
 +<td class="ntext" width="33%">
 +$\left\{\eqalign{
 +x&=\displaystyle\frac{\pi}{30}+\displaystyle\frac{2n\pi}{5}\cr
 +x&=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2n\pi}{5}} \right.$
</td> </td>
-<td class="ntext">$\textrm{e) }$</td>+<td class="ntext">f)</td>
-<td class="ntext">+<td class="ntext" width="33%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=\displaystyle\frac{\pi}{30}+\displaystyle\frac{2}{5}n\pi\cr+x&=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2n\pi}{3}\cr
-x=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2}{5}n\pi } \right.$+x&=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2n\pi}{3}} \right.$
</td> </td>
-<td class="ntext">\textrm{f) }</td> 
-<td class="ntext">$\left\{ \matrix{x=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2}{3}n\pi\cr 
-x=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2}{3}n\pi } \right.$</td> 
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 191: Rad 237:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br />[[Bild:4_4_2a-1(2).gif]]<br />[[Bild:4_4_2a-2(2).gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_2a-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_2a-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</DIV>+<div class=NavHead>L&ouml;sning b)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br />[[Bild:4_4_2b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_2b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br />[[Bild:4_4_2c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_2c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br />[[Bild:4_4_2d-1(2).gif]]<br />[[Bild:4_4_2d-2(2).gif]]+Lösning till delfråga d)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_2d-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_2d-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</DIV>+<div class=NavHead>L&ouml;sning e)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e<br />[[Bild:4_4_2e.gif]]+Lösning till delfråga e)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_2e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga f<br />[[Bild:4_4_2f.gif]]+Lösning till delfråga f)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_2f.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
-==Övning 4.4:3==+==&Ouml;vning 4.4:3==
<div class="ovning"> <div class="ovning">
Lös ekvationen Lös ekvationen
Rad 238: Rad 336:
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$\cos{x}=\cos{\left( \displaystyle \frac{\pi}{6} \right)}$</td>+<td class="ntext" width="50%">\cos{x}=\cos{\displaystyle \frac{\pi}{6}}</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$\sin{x}=\sin{\left( \displaystyle \frac{\pi}{5} \right)}$</td>+<td class="ntext" width="50%">\sin{x}=\sin{\displaystyle \frac{\pi}{5}}</td>
</tr> </tr>
-<tr align="left"><td height="5px"\></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">\sin{(x+40^\circ)}=\sin{65^\circ}</td>+<td class="ntext" width="50%">\sin{(x+40^\circ)}=\sin{65^\circ}</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">\sin{3x}=\sin{15^\circ}</td>+<td class="ntext" width="50%">\sin{3x}=\sin{15^\circ}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 256: Rad 353:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=\displaystyle\frac{\pi}{6}+2n\pi\cr+x&=\displaystyle\frac{\pi}{6}+2n\pi\cr
-x=\displaystyle\frac{11\pi}{6}+2n\pi+x&=\displaystyle\frac{11\pi}{6}+2n\pi
}\right.$ }\right.$
</td> </td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=\displaystyle\frac{\pi}{5}+2n\pi\cr+x&=\displaystyle\frac{\pi}{5}+2n\pi\cr
-x=\displaystyle\frac{4\pi}{5}+2n\pi+x&=\displaystyle\frac{4\pi}{5}+2n\pi
}\right.$ }\right.$
</td> </td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=25^\circ + n\cdot 360^\circ\cr+x&=25^\circ + n\cdot 360^\circ\cr
-x=75^\circ + n\cdot 360^\circ+x&=75^\circ + n\cdot 360^\circ
}\right.$ }\right.$
</td> </td>
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=5^\circ + n \cdot 120^\circ \cr+x&=5^\circ + n \cdot 120^\circ \cr
-x= 55^\circ + n \cdot 120^\circ+x&= 55^\circ + n \cdot 120^\circ
}\right.$ }\right.$
</td> </td>
Rad 297: Rad 393:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br />[[Bild:4_4_3a.gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_3a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</DIV>+<div class=NavHead>L&ouml;sning b)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br />[[Bild:4_4_3b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_3b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br />[[Bild:4_4_3c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_3c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br />[[Bild:4_4_3d.gif]]+Lösning till delfråga d)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_3d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
-==Övning 4.4:4==+==&Ouml;vning 4.4:4==
<div class="ovning"> <div class="ovning">
-Bestäm de vinklar v i intervallet 0^\circ \leq v \leq 360^\circ som uppfyller \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}.+Bestäm de vinklar $\,v\, i intervallet \,0^\circ \leq v \leq 360^\circ\, som uppfyller \ \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}\,$.
</div> </div>
Rad 332: Rad 456:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-v_1=50^\circ, v_2=120^\circ, v_3=230^\circ och v_4=300^\circ+<table width="100%" cellpadding="10px">
 +<tr>
 +<td align="left">
 +$v_1=50^\circ$, $\ \ v_2=120^\circ$, $\ \ v_3=230^\circ\ \ och \ \ v_4=300^\circ$
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 339: Rad 469:
<div class=NavHead>L&ouml;sning</div> <div class=NavHead>L&ouml;sning</div>
<div class=NavContent> <div class=NavContent>
-[[Bild:4_4_4-1(3).gif]]<br\>[[Bild:4_4_4-2(3).gif]]<br\>[[Bild:4_4_4-3(3).gif]]<br\>+<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_4-1(3).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_4-2(3).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_4-3(3).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
-==Övning 4.4:5==+==&Ouml;vning 4.4:5==
<div class="ovning"> <div class="ovning">
Lös ekvationen Lös ekvationen
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">\sin{3x}=\sin{x}</td>+<td class="ntext" width="50%">\sin{3x}=\sin{x}</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">\tan{x}=\tan{4x}</td>+<td class="ntext" width="50%">\tan{x}=\tan{4x}</td>
-<td class="ntext">$\textrm{c) }$</td>+</tr>
-<td class="ntext">\cos{5x}=\cos(x+\pi/5)</td>+<tr align="left">
 +<td class="ntext">c)</td>
 +<td class="ntext" width="50%">\cos{5x}=\cos(x+\pi/5)</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 362: Rad 510:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=n\pi\cr+x&=n\pi\cr
-x=\displaystyle \frac{\pi}{4}+\displaystyle \frac{1}{2}n\pi+x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
}\right.$ }\right.$
</td> </td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$x=\displaystyle \frac{1}{3}n\pi$</td>+<td class="ntext" width="50%">$x=\displaystyle \frac{n\pi}{3}$</td>
-<td class="ntext">$\textrm{c) }$</td>+</tr>
-<td class="ntext">+<tr align="left">
-$\left\{\matrix{+<td class="ntext">c)</td>
-x=\displaystyle \frac{\pi}{20}+\displaystyle \frac{1}{2}n\pi\cr+<td class="ntext" width="50%">
-x=-\displaystyle \frac{\pi}{30}+\displaystyle \frac{1}{3}n\pi+$\left\{\eqalign{
 +x&=\displaystyle \frac{\pi}{20}+\displaystyle \frac{n\pi}{2}\cr
 +x&=-\displaystyle \frac{\pi}{30}+\displaystyle \frac{n\pi}{3}
}\right.$ }\right.$
</td> </td>
Rad 388: Rad 538:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br />[[Bild:4_4_5a-1(2).gif]]<br />[[Bild:4_4_5a-2(2).gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_5a-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_5a-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</DIV>+<div class=NavHead>L&ouml;sning b)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br />[[Bild:4_4_5b-1(2).gif]]<br />[[Bild:4_4_5b-2(2).gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_5b-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_5b-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br />[[Bild:4_4_5c-1(2).gif]]<br />[[Bild:4_4_5c-2(2).gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_5c-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_5c-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
-==Övning 4.4:6==+==&Ouml;vning 4.4:6==
<div class="ovning"> <div class="ovning">
Lös ekvationen Lös ekvationen
Rad 414: Rad 600:
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">\sin x\cdot \cos 3x = 2\sin x</td>+<td class="ntext" width="50%">\sin x\cdot \cos 3x = 2\sin x</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">\sqrt{2}\sin{x}\cos{x}=\cos{x}</td>+<td class="ntext" width="50%">\sqrt{2}\sin{x}\cos{x}=\cos{x}</td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">\sin 2x = -\sin x</td>+<td class="ntext" width="50%">\sin 2x = -\sin x</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 427: Rad 615:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">+<td class="ntext" width="50%">
x=n\pi x=n\pi
</td> </td>
-<td class="ntext">$b)</td>+<td class="ntext">b)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{x=\displaystyle \frac{\pi}{4}+2n\pi\cr+$\left\{\eqalign{
-x=\displaystyle \frac{\pi}{2}+n\pi\cr+x&=\displaystyle \frac{\pi}{4}+2n\pi\cr
-x=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$+x&=\displaystyle \frac{\pi}{2}+n\pi\cr
 +x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$
</td> </td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{ +$\left\{\eqalign{
-x=\displaystyle \frac{2n\pi}{3}\cr+x&=\displaystyle \frac{2n\pi}{3}\cr
-x=\displaystyle \pi + 2n\pi\+x&=\displaystyle \pi + 2n\pi\cr
}\right.$ }\right.$
</td> </td>
Rad 454: Rad 645:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br />[[Bild:4_4_6a.gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_6a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</DIV>+<div class=NavHead>L&ouml;sning b)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br />[[Bild:4_4_6b-1(2).gif]]<br />[[Bild:4_4_6b-2(2).gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_6b-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_6b-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br />[[Bild:4_4_6c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_6c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 480: Rad 697:
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">2\sin^2{x}+\sin{x}=1</td>+<td class="ntext" width="50%">2\sin^2{x}+\sin{x}=1</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">2\sin^2{x}-3\cos{x}=0</td>+<td class="ntext" width="50%">2\sin^2{x}-3\cos{x}=0</td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">\cos{3x}=\sin{4x}</td>+<td class="ntext" width="50%">\cos{3x}=\sin{4x}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 493: Rad 712:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">+<td class="ntext" width="50%">
$\left\{ \matrix{ $\left\{ \matrix{
x=\displaystyle \frac{\pi}{6}+2n\pi\cr x=\displaystyle \frac{\pi}{6}+2n\pi\cr
Rad 505: Rad 724:
</td> </td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">x=\pm \displaystyle \frac{\pi}{3} + 2n\pi </td>+<td class="ntext" width="50%">x=\pm \displaystyle \frac{\pi}{3} + 2n\pi </td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">+<td class="ntext" width="50%">
$\left\{ \matrix{ $\left\{ \matrix{
x=\displaystyle \frac{\pi}{2}+2n\pi\cr x=\displaystyle \frac{\pi}{2}+2n\pi\cr
-x=\displaystyle \frac{\pi}{14}+\displaystyle \frac{2}{7}n\pi+x=\displaystyle \frac{\pi}{14}+\displaystyle \frac{2n\pi}{7}
}\right.$ }\right.$
</td> </td>
Rad 520: Rad 741:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br />[[Bild:4_4_7a-1(2).gif]]<br />[[Bild:4_4_7a-2(2).gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_7a-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_7a-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</DIV>+<div class=NavHead>L&ouml;sning b)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br />[[Bild:4_4_7b-1(2).gif]]<br />[[Bild:4_4_7b-2(2).gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_7b-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_7b-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br />[[Bild:4_4_7c-1(3).gif]]<br />[[Bild:4_4_7c-2(3).gif]]<br />[[Bild:4_4_7c-3(3).gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_7c-1(3).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_7c-2(3).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_7c-3(3).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 546: Rad 808:
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">\sin{2x}=\sqrt{2}\cos{x}</td>+<td class="ntext" width="50%">\sin{2x}=\sqrt{2}\cos{x}</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">\sin{x}=\sqrt{3}\cos{x}</td>+<td class="ntext" width="50%">\sin{x}=\sqrt{3}\cos{x}</td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">\displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}</td>+<td class="ntext" width="50%">\displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 559: Rad 823:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=\displaystyle \frac{\pi}{4}+2n\pi\cr+x&=\displaystyle \frac{\pi}{4}+2n\pi\cr
-x=\displaystyle \frac{\pi}{2}+n\pi\cr+x&=\displaystyle \frac{\pi}{2}+n\pi\cr
-x=\displaystyle \frac{3\pi}{4}+2n\pi+x&=\displaystyle \frac{3\pi}{4}+2n\pi
}\right.$ }\right.$
</td> </td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">x=\displaystyle \frac{\pi}{3}+n\pi</td>+<td class="ntext" width="50%">x=\displaystyle \frac{\pi}{3}+n\pi</td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">+<td class="ntext" width="50%">
-$\left\{ \matrix{+$\left\{\eqalign{
-x=n\pi\cr+x&=n\pi\cr
-x=\displaystyle \frac{3\pi}{4}+n\pi+x&=\displaystyle \frac{3\pi}{4}+n\pi
}\right.$ }\right.$
</td> </td>
Rad 586: Rad 852:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br />[[Bild:4_4_8a-1(2).gif]][[Bild:4_4_8a-2(2).gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_8a-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:4_4_8a-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</DIV>+<div class=NavHead>L&ouml;sning b)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br />[[Bild:4_4_8b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:4_4_8b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br />[[Bild:4_4_8c-1(2).gif]][[Bild:4_4_8c-2(2).gif]]+Lösning till delfråga c)
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[redigera] Övning 4.4:1

För vilka vinklar \,v\,, där \,0 \leq v\leq 2\pi\,, gäller att

a) \sin{v}=\displaystyle \frac{1}{2} b) \cos{v}=\displaystyle \frac{1}{2}
c) \sin{v}=1 d) \tan{v}=1
e) \cos{v}=2 f) \sin{v}=-\displaystyle \frac{1}{2}
g) \tan{v}=-\displaystyle \frac{1}{\sqrt{3}}

[redigera] Övning 4.4:2

Lös ekvationen

a) \sin{x}=\displaystyle \frac{\sqrt{3}}{2} b) \cos{x}=\displaystyle \frac{1}{2} c) \sin{x}=0
d) \sin{5x}=\displaystyle \frac{1}{\sqrt{2}} e) \sin{5x}=\displaystyle \frac{1}{2} f) \cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}

[redigera] Övning 4.4:3

Lös ekvationen

a) \cos{x}=\cos{\displaystyle \frac{\pi}{6}} b) \sin{x}=\sin{\displaystyle \frac{\pi}{5}}
c) \sin{(x+40^\circ)}=\sin{65^\circ} d) \sin{3x}=\sin{15^\circ}

[redigera] Övning 4.4:4

Bestäm de vinklar \,v\, i intervallet \,0^\circ \leq v \leq 360^\circ\, som uppfyller \ \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}\,.

[redigera] Övning 4.4:5

Lös ekvationen

a) \sin{3x}=\sin{x} b) \tan{x}=\tan{4x}
c) \cos{5x}=\cos(x+\pi/5)

[redigera] Övning 4.4:6

Lös ekvationen

a) \sin x\cdot \cos 3x = 2\sin x b) \sqrt{2}\sin{x}\cos{x}=\cos{x}
c) \sin 2x = -\sin x

[redigera] Övning 4.4:7

Lös ekvationen

a) 2\sin^2{x}+\sin{x}=1 b) 2\sin^2{x}-3\cos{x}=0
c) \cos{3x}=\sin{4x}

[redigera] Övning 4.4:8

Lös ekvationen

a) \sin{2x}=\sqrt{2}\cos{x} b) \sin{x}=\sqrt{3}\cos{x}
c) \displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}
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