Lösung 4.4:3d - Versionsgeschichte

Tek: Replaced figure with metapost figure

Tek — Tue, 25 Aug 2009 13:11:41 GMT

Replaced figure with metapost figure

← Nächstältere Version		Version vom 13:11, 25. Aug. 2009
Zeile 3:		Zeile 3:
	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ}\qquad\text{und}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>3x = 15^{\circ}\qquad\text{und}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.}</math>}}

-	~~[[Image~~:~~4_4_3_d~~.~~gif\|~~center]]	+	<center>{{:4.4.3d - Solution - Two unit circles with angles 15° and 165°, respectively}}</center>

	Also ist die allgemeine Lösung		Also ist die allgemeine Lösung

Markus.bez — Fri, 19 Jun 2009 14:27:11 GMT

← Nächstältere Version		Version vom 14:27, 19. Jun. 2009
Zeile 7:		Zeile 7:
	Also ist die allgemeine Lösung		Also ist die allgemeine Lösung

-	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{und}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,,</math>}}	+	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{und}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,.</math>}}

-	~~und also~~ haben ~~wir~~ die Lösung	+	Wir haben damit die Lösung

	{{Abgesetzte Formel\|\|<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{und}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{und}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}}

Martin — Tue, 07 Apr 2009 09:24:24 GMT

← Nächstältere Version		Version vom 09:24, 7. Apr. 2009
Zeile 1:		Zeile 1:
-	~~First, we observe from the unit circle that the equation has two solutions for~~ <math>0^{\circ}\le 3x\le 360^{\circ}\,</math>,	+	Wir erhalten zwei Lösungen im Intervall <math>0^{\circ}\le 3x\le 360^{\circ}\,</math>,

-	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ}\qquad\text{~~and~~}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ}\qquad\text{und}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.}</math>}}

	[[Image:4_4_3_d.gif\|center]]		[[Image:4_4_3_d.gif\|center]]

-	~~This means that all of the equation's solutions are~~	+	Also ist die allgemeine Lösung

-	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{~~and~~}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,,</math>}}	+	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{und}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,,</math>}}

-	~~for all integers ''n'', i.e.~~	+	und also haben wir die Lösung

-	{{Abgesetzte Formel\|\|<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{~~and~~}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{und}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}}

Tekbot — Wed, 22 Oct 2008 15:15:24 GMT

hat „Solution 4.4:3d“ nach „Lösung 4.4:3d“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 15:15, 22. Okt. 2008

Tekbot — Wed, 22 Oct 2008 08:59:28 GMT

Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

← Nächstältere Version		Version vom 08:59, 22. Okt. 2008
Zeile 1:		Zeile 1:
	First, we observe from the unit circle that the equation has two solutions for <math>0^{\circ}\le 3x\le 360^{\circ}\,</math>,		First, we observe from the unit circle that the equation has two solutions for <math>0^{\circ}\le 3x\le 360^{\circ}\,</math>,

-	{{~~Displayed math~~\|\|<math>3x = 15^{\circ}\qquad\text{and}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ}\qquad\text{and}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.}</math>}}

	[[Image:4_4_3_d.gif\|center]]		[[Image:4_4_3_d.gif\|center]]
Zeile 7:		Zeile 7:
	This means that all of the equation's solutions are		This means that all of the equation's solutions are

-	{{~~Displayed math~~\|\|<math>3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,,</math>}}	+	{{Abgesetzte Formel\|\|<math>3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,,</math>}}

	for all integers ''n'', i.e.		for all integers ''n'', i.e.

-	{{~~Displayed math~~\|\|<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{and}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{and}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}}

Tek — Mon, 13 Oct 2008 13:02:54 GMT

← Nächstältere Version		Version vom 13:02, 13. Okt. 2008
Zeile 1:		Zeile 1:
-	First, we observe from the unit circle that the equation has two solutions for	+	First, we observe from the unit circle that the equation has two solutions for <math>0^{\circ}\le 3x\le 360^{\circ}\,</math>,
-	<math>0^{\circ }\le ~~\text{3}x~~\le ~~\text{36}0~~^{\circ }</math>,	+
-		+
-		+
-	~~<math>3x=15^{\circ }</math>~~	+
-	~~and~~	+
-	~~<math>3x=180^{\circ }-15^{\circ }=165^{\circ }</math>~~	+

		+	{{Displayed math\|\|<math>3x = 15^{\circ}\qquad\text{and}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.}</math>}}

	[[Image:4_4_3_d.gif\|center]]		[[Image:4_4_3_d.gif\|center]]
Zeile 12:		Zeile 7:
	This means that all of the equation's solutions are		This means that all of the equation's solutions are

		+	{{Displayed math\|\|<math>3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,,</math>}}

-	~~<math>3x=15^{\circ }+n\centerdot 360^{\circ }</math>~~	+	for all integers ''n'', i.e.
-	~~and~~	+
-	~~<math>3x=165^{\circ }+n\centerdot 360^{\circ }</math>~~	+
-		+
-		+
-	for all integers	+
-	~~<math>~~n~~</math>~~, i.e.	+
-		+

-	<math>x=5^{\circ }+n\~~centerdot~~ 120^{\circ }~~</math>~~	+	{{Displayed math\|\|<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{and}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}}
-	and	+
-	~~<math>~~x=55^{\circ }+n\~~centerdot~~ 120^{\circ }</math>	+

Ian — Wed, 01 Oct 2008 09:57:58 GMT

← Nächstältere Version		Version vom 09:57, 1. Okt. 2008
Zeile 1:		Zeile 1:
-	{{~~NAVCONTENT_START~~}}	+	First, we observe from the unit circle that the equation has two solutions for
-	<~~center~~> ~~[[Image:4_4_3d.gif]]~~ </~~center~~>	+	<math>0^{\circ }\le \text{3}x\le \text{36}0^{\circ }</math>,
-	{{~~NAVCONTENT_STOP~~}}	+
		+
		+	<math>3x=15^{\circ }</math>
		+	and
		+	<math>3x=180^{\circ }-15^{\circ }=165^{\circ }</math>
		+

	[[Image:4_4_3_d.gif\|center]]		[[Image:4_4_3_d.gif\|center]]
		+
		+	This means that all of the equation's solutions are
		+
		+
		+	<math>3x=15^{\circ }+n\centerdot 360^{\circ }</math>
		+	and
		+	<math>3x=165^{\circ }+n\centerdot 360^{\circ }</math>
		+
		+
		+	for all integers
		+	<math>n</math>, i.e.
		+
		+
		+	<math>x=5^{\circ }+n\centerdot 120^{\circ }</math>
		+	and
		+	<math>x=55^{\circ }+n\centerdot 120^{\circ }</math>

Tekbot — Tue, 09 Sep 2008 10:05:03 GMT

← Nächstältere Version

Version vom 10:05, 9. Sep. 2008

Tekbot — Thu, 21 Aug 2008 07:19:39 GMT

Robot: Automated text replacement (-[[Bild: +[[Image:)

Madde — Tue, 19 Aug 2008 12:49:11 GMT