http://wiki.math.se/wikis/sf0600_0701/index.php?action=history&feed=atom&title=4.3_Trigonometriska_samband 2026-04-24T20:30:20Z Versionshistorik för denna sida på wikin MediaWiki 1.9.3 http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=2476&oldid=prev 2007-07-18T11:49:51Z

<p><span class="autocomment">Symmetrier</span></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 18 juli 2007 kl. 11.49</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;"></td><td> </td><td style="background: #eee; 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: #ffa; font-size: smaller;">Kontroll: $\ \cos 0 = \sin (0 + \pi / 2)=<span style="color: red; font-weight: bold;">0</span>\,$.</td><td>+</td><td style="background: #cfc; font-size: smaller;">Kontroll: $\ \cos 0 = \sin (0 + \pi / 2)=<span style="color: red; font-weight: bold;">1</span>\,$.</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;">==Additions- och subtraktionsformlerna och formler för dubbla vinkeln==</td><td> </td><td style="background: #eee; font-size: smaller;">==Additions- och subtraktionsformlerna och formler för dubbla vinkeln==</td></tr> </table>

KTH.SE:u1rp004j http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1973&oldid=prev 2007-05-16T07:46:13Z

<p>Lagt in text om grund- och slutprov</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 maj 2007 kl. 07.46</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 171:</strong></td> <td colspan="2" align="left"><strong>Rad 171:</strong></td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;div class=&quot;inforuta&quot;&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;div class=&quot;inforuta&quot;&gt;</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">'''Råd för inläsning'''</td><td> </td><td style="background: #eee; font-size: smaller;">'''Råd för inläsning'''</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">'''Grund- och slutprov'''</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">Efter att du har läst texten och arbetat med övningarna ska du göra grund- och slutprovet för att bli godkänd på detta avsnitt. Du hittar länken till proven i din student lounge.</td></tr> <tr><td colspan="2">&nbsp;</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;">'''Tänk på att:'''</td><td> </td><td style="background: #eee; font-size: smaller;">'''Tänk på att:'''</td></tr> </table>

Tek http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1919&oldid=prev 2007-05-14T14:58:53Z

<p><span class="autocomment">Teori</span></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 14 maj 2007 kl. 14.58</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 81:</strong></td> <td colspan="2" align="left"><strong>Rad 81:</strong></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;">| width=50% valign=top |</td><td> </td><td style="background: #eee; font-size: smaller;">| width=50% valign=top |</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:t_3_4_1]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:t_3_4_1<span style="color: red; font-weight: bold;">.gif</span>]]</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">| width=45% valign=top |</td><td> </td><td style="background: #eee; font-size: smaller;">| width=45% valign=top |</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;br&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;br&gt;</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;">|- </td><td> </td><td style="background: #eee; font-size: smaller;">|- </td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">| width=50% valign=top |</td><td> </td><td style="background: #eee; font-size: smaller;">| width=50% valign=top |</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:t_3_4_2]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:t_3_4_2<span style="color: red; font-weight: bold;">.gif</span>]]</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">| width=40% valign=top |</td><td> </td><td style="background: #eee; font-size: smaller;">| width=40% valign=top |</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;br&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;br&gt;</td></tr> </table>

Lina http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1916&oldid=prev 2007-05-14T14:55:30Z

<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 14 maj 2007 kl. 14.55</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;">|- </td><td> </td><td style="background: #eee; font-size: smaller;">|- </td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">| width=50% valign=top |</td><td> </td><td style="background: #eee; font-size: smaller;">| width=50% valign=top |</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Bild: <span style="color: red; font-weight: bold;">figur 3.4.2</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">[[</span>Bild:<span style="color: red; font-weight: bold;">t_3_4_2]]</span></td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">| width=40% valign=top |</td><td> </td><td style="background: #eee; font-size: smaller;">| width=40% valign=top |</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;br&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;br&gt;</td></tr> </table>

Lina http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1913&oldid=prev 2007-05-14T14:53:21Z

<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 14 maj 2007 kl. 14.53</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 197:</strong></td> <td colspan="2" align="left"><strong>Rad 197:</strong></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;">&lt;/div&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;teori&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">----</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:sommarens_fluga_copyright.gif|alt Sommarens fluga - plugga matematik på nätet! Till detta kursmaterial finns prov och lärare på Internet. </td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Ger studiepoäng. Kostnadsfritt. Fortlöpande anmälan på www.math.se.</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Eftertryck förbjudet utan tillåtelse. © 2007 MATH.SE</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">]] </td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</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;">&lt;!-- slut teori --&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;!-- slut teori --&gt;</td></tr> </table>

Lina http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1894&oldid=prev 2007-05-14T14:45:10Z

<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 14 maj 2007 kl. 14.45</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 81:</strong></td> <td colspan="2" align="left"><strong>Rad 81:</strong></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;">| width=50% valign=top |</td><td> </td><td style="background: #eee; font-size: smaller;">| width=50% valign=top |</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Bild: <span style="color: red; font-weight: bold;">figur 3.4.1</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">[[</span>Bild:<span style="color: red; font-weight: bold;">t_3_4_1]]</span></td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">| width=45% valign=top |</td><td> </td><td style="background: #eee; font-size: smaller;">| width=45% valign=top |</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;br&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;br&gt;</td></tr> </table>

Lina http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1881&oldid=prev 2007-05-14T12:32:56Z

<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 14 maj 2007 kl. 12.32</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 199:</strong></td> <td colspan="2" align="left"><strong>Rad 199:</strong></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;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;<span style="color: red; font-weight: bold;">small</span>&gt;<span style="color: red; font-weight: bold;">© Copyright 2007, </span>math.se&lt;/<span style="color: red; font-weight: bold;">small</span>&gt;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;<span style="color: red; font-weight: bold;">div class=&quot;teori&quot;</span>&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">----</span></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&#160;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">[[Bild:sommarens_fluga_copyright.gif|alt Sommarens fluga - plugga matematik på nätet! Till detta kursmaterial finns prov och lärare på Internet. </span></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">Ger studiepoäng. Kostnadsfritt. Fortlöpande anmälan på www.</span>math.se<span style="color: red; font-weight: bold;">.</span></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">Eftertryck förbjudet utan tillåtelse. © 2007 MATH.SE</span></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">]] </span></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/<span style="color: red; font-weight: bold;">div</span>&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&#160;</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;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr> </table>

Lina http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1642&oldid=prev 2007-05-10T15:06:40Z

<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 10 maj 2007 kl. 15.06</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 4:</strong></td> <td colspan="2" align="left"><strong>Rad 4:</strong></td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;div class=&quot;inforuta&quot;&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;div class=&quot;inforuta&quot;&gt;</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">'''Innehåll:'''</td><td> </td><td style="background: #eee; font-size: smaller;">'''Innehåll:'''</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">*Trigonometriska <span style="color: red; font-weight: bold;">samband</span></td><td>+</td><td style="background: #cfc; font-size: smaller;">*Trigonometriska <span style="color: red; font-weight: bold;">ettan</span></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">*Formeln för dubbla och halva vinkeln</span></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">*Additions- och subtraktionsformlerna</span></td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;/div&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;/div&gt;</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 colspan="2" align="left"><strong>Rad 12:</strong></td> <td colspan="2" align="left"><strong>Rad 14:</strong></td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">Efter detta avsnitt ska du ha lärt dig att:</td><td> </td><td style="background: #eee; font-size: smaller;">Efter detta avsnitt ska du ha lärt dig att:</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">*Härleda trigonometriska samband från symmetrier i enhetscirkeln.</td><td> </td><td style="background: #eee; font-size: smaller;">*Härleda trigonometriska samband från symmetrier i enhetscirkeln.</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">*<span style="color: red; font-weight: bold;">Skriva upp (utantill) och använda följande </span>trigonometriska <span style="color: red; font-weight: bold;">samband: </span>trigonometriska <span style="color: red; font-weight: bold;">ettan, additions- och subtraktionsformler, dubbla och halva vinkeln</span>.</td><td>+</td><td style="background: #cfc; font-size: smaller;">*<span style="color: red; font-weight: bold;">Förenkla </span>trigonometriska <span style="color: red; font-weight: bold;">uttryck med hjälp av de </span>trigonometriska <span style="color: red; font-weight: bold;">sambanden</span>.</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&#160;</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;/div&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr> </table>

Tek http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1570&oldid=prev 2007-05-10T09:50:14Z

<p>En del ändringar</p> <a href="http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&amp;diff=1570&amp;oldid=1545">(Skillnad mellan versioner)</a>

Tek http://wiki.math.se/wikis/sf0600_0701/index.php?title=4.3_Trigonometriska_samband&diff=1545&oldid=prev 2007-05-07T14:03:53Z

<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 7 maj 2007 kl. 14.03</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 186:</strong></td> <td colspan="2" align="left"><strong>Rad 186:</strong></td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">$$\cos^2\frac{v}{2}= \frac{1 + \cos v}{2}$$</td><td> </td><td style="background: #eee; font-size: smaller;">$$\cos^2\frac{v}{2}= \frac{1 + \cos v}{2}$$</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;/div&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[4.3 Övningar|Övningar]]</td></tr> <tr><td colspan="2">&nbsp;</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;">&lt;div class=&quot;inforuta&quot;&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;div class=&quot;inforuta&quot;&gt;</td></tr> </table>

Lina