Lösung 4.2:3d - Versionsgeschichte

Tek: Replaced figure with metapost figure

Tek — Fri, 21 Aug 2009 08:51:03 GMT

Replaced figure with metapost figure

← Nächstältere Version		Version vom 08:51, 21. Aug. 2009
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	<math>0</math> und daher ist <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.		<math>0</math> und daher ist <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.

-	~~[[Image~~:~~4_2_3_d~~.~~gif\|~~center]]	+	<center>{{:4.2.3d - Solution - The unit circle with angle 3π/2 and point (0,-1)}}</center>

Markus.bez um 10:30, 18. Jun. 2009

Markus.bez — Thu, 18 Jun 2009 10:30:34 GMT

← Nächstältere Version		Version vom 10:30, 18. Jun. 2009
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-	Wir subtrahieren <math>2\pi</math> vom Winkel math>{7\pi }/{2}\,</math>, so oft bis wir einen Winkel zwischen <math>0</math> und <math>2\pi</math> erhalten,	+	Wir subtrahieren <math>2\pi</math> vom Winkel <math>{7\pi }/{2}\,</math> so oft, bis wir einen Winkel zwischen <math>0</math> und <math>2\pi</math> erhalten:

	{{Abgesetzte Formel\|\|<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}

-	Wir sehen dass die Gerade mit den Winkel <math>3\pi/2</math> zur ''x''-Achse den Einheitskreis im Punkt (0,-1) schneidet. Die ''x''-Koordinate des Schnittpunktes ist also	+	Wir sehen, dass die Gerade mit den Winkel <math>3\pi/2</math> zur ''x''-Achse den Einheitskreis im Punkt (0,-1) schneidet. Die ''x''-Koordinate des Schnittpunktes ist also
	<math>0</math> und daher ist <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.		<math>0</math> und daher ist <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.

	[[Image:4_2_3_d.gif\|center]]		[[Image:4_2_3_d.gif\|center]]

Martin um 12:32, 4. Apr. 2009

Martin — Sat, 04 Apr 2009 12:32:36 GMT

← Nächstältere Version		Version vom 12:32, 4. Apr. 2009
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-	~~In order to get an angle between~~ <math>0</math> ~~and <~~math>\~~text~~{2}\pi</math>, ~~we subtract~~ <math>~~2\pi~~</math> ~~from~~ <math>{7\pi ~~}/{2}\,~~</math>, ~~which also leaves the cosine value unchanged~~	+	Wir subtrahieren <math>2\pi</math> vom Winkel math>{7\pi }/{2}\,</math>, so oft bis wir einen Winkel zwischen <math>0</math> und <math>2\pi</math> erhalten,

	{{Abgesetzte Formel\|\|<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}

-	~~When we draw a line which makes an angle~~ <math>3\pi/2</math> ~~with the positive~~ ''x''-~~axis, we get the negative ''y''-axis and we see that this line cuts the unit circle at the point~~ (0,-1). ~~The~~ ''x''-~~coordinate of the intersection point is thus~~	+	Wir sehen dass die Gerade mit den Winkel <math>3\pi/2</math> zur ''x''-Achse den Einheitskreis im Punkt (0,-1) schneidet. Die ''x''-Koordinate des Schnittpunktes ist also
-	<math>0</math> ~~and hence~~ <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.	+	<math>0</math> und daher ist <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.

	[[Image:4_2_3_d.gif\|center]]		[[Image:4_2_3_d.gif\|center]]

Tekbot: hat „Solution 4.2:3d“ nach „Lösung 4.2:3d“ verschoben: Robot: moved page

Tekbot — Wed, 22 Oct 2008 14:55:04 GMT

hat „Solution 4.2:3d“ nach „Lösung 4.2:3d“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 14:55, 22. Okt. 2008

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

Tekbot — Wed, 22 Oct 2008 08:51:48 GMT

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

← Nächstältere Version		Version vom 08:51, 22. Okt. 2008
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	In order to get an angle between <math>0</math> and <math>\text{2}\pi</math>, we subtract <math>2\pi</math> from <math>{7\pi }/{2}\,</math>, which also leaves the cosine value unchanged		In order to get an angle between <math>0</math> and <math>\text{2}\pi</math>, we subtract <math>2\pi</math> from <math>{7\pi }/{2}\,</math>, which also leaves the cosine value unchanged

-	{{~~Displayed math~~\|\|<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}

	When we draw a line which makes an angle <math>3\pi/2</math> with the positive ''x''-axis, we get the negative ''y''-axis and we see that this line cuts the unit circle at the point (0,-1). The ''x''-coordinate of the intersection point is thus		When we draw a line which makes an angle <math>3\pi/2</math> with the positive ''x''-axis, we get the negative ''y''-axis and we see that this line cuts the unit circle at the point (0,-1). The ''x''-coordinate of the intersection point is thus

Tek um 07:57, 9. Okt. 2008

Tek — Thu, 09 Oct 2008 07:57:34 GMT

← Nächstältere Version		Version vom 07:57, 9. Okt. 2008
Zeile 1:		Zeile 1:
-	In order to get an angle between	+	In order to get an angle between <math>0</math> and <math>\text{2}\pi</math>, we subtract <math>2\pi</math> from <math>{7\pi }/{2}\,</math>, which also leaves the cosine value unchanged
-	<math>0</math>	+
-	and	+
-	<math>\text{2}\pi </math>, we subtract	+
-	<math>~~\text{~~2}\pi </math>	+
-	from	+
-	<math>{7\pi }/{2}\;</math>	+
-	, which also leaves the cosine value unchanged	+
-		+
-		+
-	~~<math>\cos \frac{7\pi }{2}=\cos \left( \frac{7\pi }{2}-2\pi \right)=\cos \frac{3\pi }{2}</math>~~	+
-		+
-		+
-	~~When we draw a line which makes an angle~~	+
-	~~<math>{3\pi }/{2}\;</math>~~	+
-	~~with the positive~~	+
-	~~<math>x</math>~~	+
-	~~-axis, we get the negative~~	+
-	~~<math>y</math>~~	+
-	~~-axis and we see that this line cuts the unit circle at the point~~	+
-	~~<math>\left( 0 \right.,\left. -1 \right)</math>. The~~	+
-	~~<math>x</math>~~	+
-	~~-coordinate of the intersection point is thus~~	+
-	~~<math>0</math>~~	+
-	~~and hence~~	+
-	~~<math>\cos {7\pi }/{2}\;=\cos {3\pi }/{2}\;=0</math>~~	+

		+	{{Displayed math\|\|<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}

		+	When we draw a line which makes an angle <math>3\pi/2</math> with the positive ''x''-axis, we get the negative ''y''-axis and we see that this line cuts the unit circle at the point (0,-1). The ''x''-coordinate of the intersection point is thus
		+	<math>0</math> and hence <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.

	[[Image:4_2_3_d.gif\|center]]		[[Image:4_2_3_d.gif\|center]]

Ian um 12:06, 28. Sep. 2008

Ian — Sun, 28 Sep 2008 12:06:44 GMT

← Nächstältere Version		Version vom 12:06, 28. Sep. 2008
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-	{{~~NAVCONTENT_START~~}}	+	In order to get an angle between
-	<~~center~~> ~~[[Image:4_2_3d~~.~~gif]]~~ </~~center~~>	+	<math>0</math>
-	{{~~NAVCONTENT_STOP~~}}	+	and
		+	<math>\text{2}\pi </math>, we subtract
		+	<math>\text{2}\pi </math>
		+	from
		+	<math>{7\pi }/{2}\;</math>
		+	, which also leaves the cosine value unchanged
		+
		+
		+	<math>\cos \frac{7\pi }{2}=\cos \left( \frac{7\pi }{2}-2\pi \right)=\cos \frac{3\pi }{2}</math>
		+
		+
		+	When we draw a line which makes an angle
		+	<math>{3\pi }/{2}\;</math>
		+	with the positive
		+	<math>x</math>
		+	-axis, we get the negative
		+	<math>y</math>
		+	-axis and we see that this line cuts the unit circle at the point
		+	<math>\left( 0 \right.,\left. -1 \right)</math>. The
		+	<math>x</math>
		+	-coordinate of the intersection point is thus
		+	<math>0</math>
		+	and hence
		+	<math>\cos {7\pi }/{2}\;=\cos {3\pi }/{2}\;=0</math>
		+
		+
		+
	[[Image:4_2_3_d.gif\|center]]		[[Image:4_2_3_d.gif\|center]]

Tekbot: Lösning 4.2:3d moved to Solution 4.2:3d: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:44:43 GMT

Lösning 4.2:3d moved to Solution 4.2:3d: Robot: moved page

← Nächstältere Version

Version vom 09:44, 9. Sep. 2008

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

Tekbot — Thu, 21 Aug 2008 07:09:29 GMT

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

← Nächstältere Version		Version vom 07:09, 21. Aug. 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:4_2_3d.gif]] </center>	+	<center> [[Image:4_2_3d.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}
-	[[~~Bild~~:4_2_3_d.gif\|center]]	+	[[Image:4_2_3_d.gif\|center]]

Madde um 14:29, 15. Aug. 2008

Madde — Fri, 15 Aug 2008 14:29:46 GMT

← Nächstältere Version		Version vom 14:29, 15. Aug. 2008
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	<center> [[Bild:4_2_3d.gif]] </center>		<center> [[Bild:4_2_3d.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}
		+	[[Bild:4_2_3_d.gif\|center]]