Lösung 4.3:3e - Versionsgeschichte

Tek um 08:13, 25. Aug. 2009

Tek — Tue, 25 Aug 2009 08:13:39 GMT

← Nächstältere Version		Version vom 08:13, 25. Aug. 2009
Zeile 5:		Zeile 5:
	{\| align="center"		{\| align="center"
	\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle v}}		\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle v}}
		+	\|width="20px"\|
	\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle π/2 + v}}		\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle π/2 + v}}
	\|-		\|-
	\|align="center"\|<small>Winkel ''v''</small>		\|align="center"\|<small>Winkel ''v''</small>
		+	\|\|
	\|align="center"\|<small>Winkel π/2 + ''v''</small>		\|align="center"\|<small>Winkel π/2 + ''v''</small>
	\|}		\|}

Tek: Replaced figures with metapost figures

Tek — Tue, 25 Aug 2009 08:08:45 GMT

Replaced figures with metapost figures

← Nächstältere Version		Version vom 08:08, 25. Aug. 2009
Zeile 4:		Zeile 4:

	{\| align="center"		{\| align="center"
-	\|align="center"\|~~[[Image~~:~~4_3_3_e-1~~.~~gif\|center]]~~	+	\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle v}}
-	\|align="center"\|~~[[Image~~:~~4_3_3_e~~-2~~.gif\|center]]~~	+	\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle π/2 + v}}
	\|-		\|-
	\|align="center"\|<small>Winkel ''v''</small>		\|align="center"\|<small>Winkel ''v''</small>
	\|align="center"\|<small>Winkel π/2 + ''v''</small>		\|align="center"\|<small>Winkel π/2 + ''v''</small>
	\|}		\|}

Bayerer um 14:46, 27. Jul. 2009

Bayerer — Mon, 27 Jul 2009 14:46:46 GMT

← Nächstältere Version		Version vom 14:46, 27. Jul. 2009
Zeile 7:		Zeile 7:
	\|align="center"\|[[Image:4_3_3_e-2.gif\|center]]		\|align="center"\|[[Image:4_3_3_e-2.gif\|center]]
	\|-		\|-
-	\|align="center"\|<small>~~Angle~~ ''v''</small>	+	\|align="center"\|<small>Winkel ''v''</small>
-	\|align="center"\|<small>~~Angle~~ π/2 + ''v''</small>	+	\|align="center"\|<small>Winkel π/2 + ''v''</small>
	\|}		\|}

Markus.bez um 09:43, 19. Jun. 2009

Markus.bez — Fri, 19 Jun 2009 09:43:59 GMT

← Nächstältere Version		Version vom 09:43, 19. Jun. 2009
Zeile 1:		Zeile 1:
-	Der Winkel <math>\pi/2+v</math> hat denselben Winkel zur positiven ''y''-Achse, wie der Winkel <math>v</math> zur positiven ''x''-Achse ~~hat~~. Also ist die ''x''-Koordinate des Winkels <math>\pi/2+v</math> dieselbe wie die ''y''-Koordinate des Winkels <math>v</math>, aber mit ~~anderen~~ Vorzeichen.	+	Der Winkel <math>\pi/2+v</math> hat denselben Winkel zur positiven ''y''-Achse wie der Winkel <math>v</math> zur positiven ''x''-Achse. Also ist die ''x''-Koordinate des Winkels <math>\pi/2+v</math> dieselbe wie die ''y''-Koordinate des Winkels <math>v</math>, aber mit umgekehrtem Vorzeichen.

	{{Abgesetzte Formel\|\|<math>\cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}</math>}}

Martin um 12:20, 5. Apr. 2009

Martin — Sun, 05 Apr 2009 12:20:21 GMT

← Nächstältere Version		Version vom 12:20, 5. Apr. 2009
Zeile 1:		Zeile 1:
-	~~The angle~~ <math>\pi/2+v</math> ~~makes the same angle with the positive~~ ''y''-~~axis as the angle ''~~v~~'' makes with the positive~~ ''x''-~~axis, and hence we see that the~~ ''x''-~~coordinate for~~ <math>\pi/2+v</math> ~~is equal to the~~ ''y''-~~coordinate for ''~~v'', ~~but with a change of sign, i.e~~.	+	Der Winkel <math>\pi/2+v</math> hat denselben Winkel zur positiven ''y''-Achse, wie der Winkel <math>v</math> zur positiven ''x''-Achse hat. Also ist die ''x''-Koordinate des Winkels <math>\pi/2+v</math> dieselbe wie die ''y''-Koordinate des Winkels <math>v</math>, aber mit anderen Vorzeichen.

	{{Abgesetzte Formel\|\|<math>\cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}</math>}}

Tekbot: hat „Solution 4.3:3e“ nach „Lösung 4.3:3e“ verschoben: Robot: moved page

Tekbot — Wed, 22 Oct 2008 15:03:44 GMT

hat „Solution 4.3:3e“ nach „Lösung 4.3:3e“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 15:03, 22. Okt. 2008

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

Tekbot — Wed, 22 Oct 2008 08:54:38 GMT

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

← Nächstältere Version		Version vom 08:54, 22. Okt. 2008
Zeile 1:		Zeile 1:
	The angle <math>\pi/2+v</math> makes the same angle with the positive ''y''-axis as the angle ''v'' makes with the positive ''x''-axis, and hence we see that the ''x''-coordinate for <math>\pi/2+v</math> is equal to the ''y''-coordinate for ''v'', but with a change of sign, i.e.		The angle <math>\pi/2+v</math> makes the same angle with the positive ''y''-axis as the angle ''v'' makes with the positive ''x''-axis, and hence we see that the ''x''-coordinate for <math>\pi/2+v</math> is equal to the ''y''-coordinate for ''v'', but with a change of sign, i.e.

-	{{~~Displayed math~~\|\|<math>\cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}</math>}}

	{\| align="center"		{\| align="center"

Tek um 12:22, 10. Okt. 2008

Tek — Fri, 10 Oct 2008 12:22:10 GMT

← Nächstältere Version		Version vom 12:22, 10. Okt. 2008
Zeile 1:		Zeile 1:
-	The angle	+	The angle <math>\pi/2+v</math> makes the same angle with the positive ''y''-axis as the angle ''v'' makes with the positive ''x''-axis, and hence we see that the ''x''-coordinate for <math>\pi/2+v</math> is equal to the ''y''-coordinate for ''v'', but with a change of sign, i.e.
-	<math>~~\frac{~~\pi }{2}+v</math>	+
-	makes the same angle with the positive	+
-	~~<math>~~y~~</math>~~	+
-	-axis as the angle	+
-	~~<math>~~v~~</math>~~	+
-	makes with the positive	+
-	~~<math>~~x~~</math>~~	+
-	-axis, and hence we see that the	+
-	~~<math>~~x~~</math>~~	+
-	-coordinate for	+
-	<math>~~\frac{~~\pi }{2}+v</math>	+
-	is equal to the	+
-	~~<math>~~y~~</math>~~	+
-	-coordinate for	+
-	~~<math>~~v~~</math>~~, but with a change of sign, i.e.	+

		+	{{Displayed math\|\|<math>\cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}</math>}}

-	~~<math>\cos \left( \frac~~{~~\pi }{2}+v \right)~~=~~-\sin v=-a</math>~~	+	{\| align="center"
-		+	\|align="center"\|[[Image:4_3_3_e-1.gif\|center]]
-	[[Image:4_3_3_e-1.gif\|center]][[Image:4_3_3_e-2.gif\|center]]	+	\|align="center"\|[[Image:4_3_3_e-2.gif\|center]]
-		+	\|-
-		+	\|align="center"\|<small>Angle ''v''</small>
-	~~angle~~	+	\|align="center"\|<small>Angle π/2 + ''v''</small>
-	<~~math~~>v</~~math~~>	+	\|}
-	~~angle~~	+
-	<~~math~~>~~\frac{\pi }{~~2}+v</~~math~~>	+

Ian um 09:12, 10. Okt. 2008

Ian — Fri, 10 Oct 2008 09:12:57 GMT

← Nächstältere Version		Version vom 09:12, 10. Okt. 2008
Zeile 1:		Zeile 1:
-	{{~~NAVCONTENT_START}~~}	+	The angle
-	<~~center~~> ~~[[Image:4_3_3e.gif]]~~ </~~center~~>	+	<math>\frac{\pi }{2}+v</math>
-	{{~~NAVCONTENT_STOP~~}}	+	makes the same angle with the positive
		+	<math>y</math>
		+	-axis as the angle
		+	<math>v</math>
		+	makes with the positive
		+	<math>x</math>
		+	-axis, and hence we see that the
		+	<math>x</math>
		+	-coordinate for
		+	<math>\frac{\pi }{2}+v</math>
		+	is equal to the
		+	<math>y</math>
		+	-coordinate for
		+	<math>v</math>, but with a change of sign, i.e.
		+
		+
		+	<math>\cos \left( \frac{\pi }{2}+v \right)=-\sin v=-a</math>

	[[Image:4_3_3_e-1.gif\|center]][[Image:4_3_3_e-2.gif\|center]]		[[Image:4_3_3_e-1.gif\|center]][[Image:4_3_3_e-2.gif\|center]]
		+
		+
		+	angle
		+	<math>v</math>
		+	angle
		+	<math>\frac{\pi }{2}+v</math>

Tek um 13:51, 9. Okt. 2008

Tek — Thu, 09 Oct 2008 13:51:43 GMT

← Nächstältere Version		Version vom 13:51, 9. Okt. 2008
Zeile 3:		Zeile 3:
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

-	[[Image:4_3_3_e.gif\|center]]	+	[[Image:4_3_3_e-1.gif\|center]][[Image:4_3_3_e-2.gif\|center]]

← Nächstältere Version		Version vom 08:13, 25. Aug. 2009
Zeile 5:		Zeile 5:
	{\| align="center"		{\| align="center"
	\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle v}}		\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle v}}
		+	\|width="20px"\|
	\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle π/2 + v}}		\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle π/2 + v}}
	\|-		\|-
	\|align="center"\|<small>Winkel ''v''</small>		\|align="center"\|<small>Winkel ''v''</small>
		+	\|\|
	\|align="center"\|<small>Winkel π/2 + ''v''</small>		\|align="center"\|<small>Winkel π/2 + ''v''</small>
	\|}		\|}

← Nächstältere Version		Version vom 08:08, 25. Aug. 2009
Zeile 4:		Zeile 4:

	{\| align="center"		{\| align="center"
-	\|align="center"\|~~[[Image~~:~~4_3_3_e-1~~.~~gif\|center]]~~	+	\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle v}}
-	\|align="center"\|~~[[Image~~:~~4_3_3_e~~-2~~.gif\|center]]~~	+	\|align="center"\|{{:4.3.3e - Solution - The unit circle with angle π/2 + v}}
	\|-		\|-
	\|align="center"\|<small>Winkel ''v''</small>		\|align="center"\|<small>Winkel ''v''</small>
	\|align="center"\|<small>Winkel π/2 + ''v''</small>		\|align="center"\|<small>Winkel π/2 + ''v''</small>
	\|}		\|}