Lösung 4.2:5d - Versionsgeschichte

Markus.bez um 13:27, 18. Jun. 2009

Markus.bez — Thu, 18 Jun 2009 13:27:13 GMT

← Nächstältere Version		Version vom 13:27, 18. Jun. 2009
Zeile 1:		Zeile 1:
-	Indem wir 360° von 495° subtrahieren ändern wir nicht den Wert des Tangens	+	Indem wir 360° von 495° subtrahieren, ändern wir nicht den Wert des Tangens

	{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}

-	Von ~~der~~ Übung a wissen wir dass <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> und <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>~~, und wir~~ erhalten also	+	Von Übung a wissen wir, dass <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> und <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>. Wir erhalten also

	{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}

Martin um 16:05, 4. Apr. 2009

Martin — Sat, 04 Apr 2009 16:05:38 GMT

← Nächstältere Version		Version vom 16:05, 4. Apr. 2009
Zeile 3:		Zeile 3:
	{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}

-	Von der Übung a wissen wir dass	+	Von der Übung a wissen wir dass <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> und <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>, und wir erhalten also
-		+
-	<math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> und	+
-		+
-	<math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>,	+
-		+
-	und wir erhalten also	+

	{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}

Martin um 16:05, 4. Apr. 2009

Martin — Sat, 04 Apr 2009 16:05:14 GMT

← Nächstältere Version		Version vom 16:05, 4. Apr. 2009
Zeile 3:		Zeile 3:
	{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}

-	Von der Übung a wissen wir dass <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> und <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>, und wir erhalten also	+	Von der Übung a wissen wir dass
		+
		+	<math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> und
		+
		+	<math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>,
		+
		+	und wir erhalten also

	{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}

Martin um 16:04, 4. Apr. 2009

Martin — Sat, 04 Apr 2009 16:04:44 GMT

← Nächstältere Version		Version vom 16:04, 4. Apr. 2009
Zeile 1:		Zeile 1:
-	~~By subtracting~~ 360° ~~from~~ 495°~~, we do not change the value of the tangent,~~	+	Indem wir 360° von 495° subtrahieren ändern wir nicht den Wert des Tangens

	{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}

-	~~We know from exercise~~ a ~~that~~ <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> ~~and~~ <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>, ~~which gives~~	+	Von der Übung a wissen wir dass <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> und <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>, und wir erhalten also

	{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}

Tekbot: hat „Solution 4.2:5d“ nach „Lösung 4.2:5d“ verschoben: Robot: moved page

Tekbot — Wed, 22 Oct 2008 14:59:04 GMT

hat „Solution 4.2:5d“ nach „Lösung 4.2:5d“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 14:59, 22. Okt. 2008

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

Tekbot — Wed, 22 Oct 2008 08:53:18 GMT

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

← Nächstältere Version		Version vom 08:53, 22. Okt. 2008
Zeile 1:		Zeile 1:
	By subtracting 360° from 495°, we do not change the value of the tangent,		By subtracting 360° from 495°, we do not change the value of the tangent,

-	{{~~Displayed math~~\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}

	We know from exercise a that <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> and <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>, which gives		We know from exercise a that <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> and <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>, which gives

-	{{~~Displayed math~~\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}

Tek um 11:15, 9. Okt. 2008

Tek — Thu, 09 Oct 2008 11:15:18 GMT

← Nächstältere Version		Version vom 11:15, 9. Okt. 2008
Zeile 1:		Zeile 1:
-	By subtracting	+	By subtracting 360° from 495°, we do not change the value of the tangent,
-	~~<math>360^{\circ }</math>~~	+
-	from	+
-	~~<math>\text{495}^{\circ }</math>~~, we do not change the value of the tangent:	+

		+	{{Displayed math\|\|<math>\tan 495^{\circ} = \tan (495^{\circ} - 360^{\circ}) = \tan 135^{\circ}\,\textrm{.}</math>}}

-	<math>\~~tan \text{495}~~^{\circ }=\~~tan~~ \~~left( \text~~{~~495~~}^{\~~circ }-360~~^{\circ } ~~\right)~~=\~~tan~~ \~~text~~{~~135~~}^{\~~circ }~~</math>	+	We know from exercise a that <math>\cos 135^{\circ} = -1/\!\sqrt{2}</math> and <math>\sin 135^{\circ} = 1/\!\sqrt{2}\,</math>, which gives

-	~~We know from exercise a that~~	+	{{Displayed math\|\|<math>\tan 135^{\circ} = \frac{\sin 135^{\circ}}{\cos 135^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}
-	~~<math>\cos 135^~~{~~\circ }=-\frac~~{~~1}{\sqrt{2}}</~~math>	+
-	~~and~~	+
-	~~<math>\sin 135^{\circ }=\frac{1}{\sqrt{2}}</math>, which gives~~	+
-		+
-		+
-	<math>\tan 135^{\circ }=\frac{\sin 135^{\circ }}{\cos 135^{\circ }}=\frac{\~~frac~~{1}{\sqrt{2}}}{-\~~frac~~{1}{\sqrt{2}}}=-1</math>	+

Ian um 08:16, 29. Sep. 2008

Ian — Mon, 29 Sep 2008 08:16:18 GMT

← Nächstältere Version		Version vom 08:16, 29. Sep. 2008
Zeile 1:		Zeile 1:
-	{{~~NAVCONTENT_START~~}}	+	By subtracting
-	<~~center~~> ~~[[Image~~:~~4_2_5d.gif]]~~ </~~center~~>	+	<math>360^{\circ }</math>
-	{{~~NAVCONTENT_STOP~~}}	+	from
		+	<math>\text{495}^{\circ }</math>, we do not change the value of the tangent:
		+
		+
		+	<math>\tan \text{495}^{\circ }=\tan \left( \text{495}^{\circ }-360^{\circ } \right)=\tan \text{135}^{\circ }</math>
		+
		+	We know from exercise a that
		+	<math>\cos 135^{\circ }=-\frac{1}{\sqrt{2}}</math>
		+	and
		+	<math>\sin 135^{\circ }=\frac{1}{\sqrt{2}}</math>, which gives
		+
		+
		+	<math>\tan 135^{\circ }=\frac{\sin 135^{\circ }}{\cos 135^{\circ }}=\frac{\frac{1}{\sqrt{2}}}{-\frac{1}{\sqrt{2}}}=-1</math>

Tekbot: Lösning 4.2:5d moved to Solution 4.2:5d: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:48:43 GMT

Lösning 4.2:5d moved to Solution 4.2:5d: Robot: moved page

← Nächstältere Version

Version vom 09:48, 9. Sep. 2008

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

Tekbot — Thu, 21 Aug 2008 07:11:29 GMT

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

← Nächstältere Version		Version vom 07:11, 21. Aug. 2008
Zeile 1:		Zeile 1:
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:4_2_5d.gif]] </center>	+	<center> [[Image:4_2_5d.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}