Lösung 4.4:8b - Versionsgeschichte

Markus.bez um 15:03, 19. Jun. 2009

2009-06-19T15:03:56Z

← Nächstältere Version		Version vom 15:03, 19. Jun. 2009
Zeile 1:		Zeile 1:
-	Falls <math>\cos x\ne 0</math>, können wir beide Seiten durch <math>\cos x</math> dividieren,	+	Falls <math>\cos x\ne 0</math> können wir beide Seiten durch <math>\cos x</math> dividieren:

	{{Abgesetzte Formel\|\|<math>\frac{\sin x}{\cos x} = \sqrt{3}\qquad\text{i.e.}\qquad \tan x = \sqrt{3}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\frac{\sin x}{\cos x} = \sqrt{3}\qquad\text{i.e.}\qquad \tan x = \sqrt{3}\,\textrm{.}</math>}}

-	Diese Gleichung hat die Lösungen <math>x = \pi/3+n\pi</math>	+	Diese Gleichung hat die Lösungen <math>x = \pi/3+n\pi.</math>

-	Falls <math>\cos x=0</math>, ist <math>\sin x = \pm 1</math> (~~durch den~~ Einheitskreis)~~, und diese~~ Gleichung hat also keine Lösung	+	Falls <math>\cos x=0</math>, ist <math>\sin x = \pm 1</math> (auf dem Einheitskreis). Diese Gleichung hat also keine Lösung.

	Also haben wir nur die Lösung		Also haben wir nur die Lösung

-	{{Abgesetzte Formel\|\|<math>x = \frac{\pi}{3}+n\pi\~~qquad~~</math>}}	+	{{Abgesetzte Formel\|\|<math>x = \frac{\pi}{3}+n\pi\,.</math>}}

2009-04-07T12:13:19Z

← Nächstältere Version		Version vom 12:13, 7. Apr. 2009
Zeile 1:		Zeile 1:
-	~~Suppose that~~ <math>\cos x\ne 0</math>, ~~so that we can divide both sides by~~ <math>\cos x</math> ~~to obtain~~	+	Falls <math>\cos x\ne 0</math>, können wir beide Seiten durch <math>\cos x</math> dividieren,

	{{Abgesetzte Formel\|\|<math>\frac{\sin x}{\cos x} = \sqrt{3}\qquad\text{i.e.}\qquad \tan x = \sqrt{3}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\frac{\sin x}{\cos x} = \sqrt{3}\qquad\text{i.e.}\qquad \tan x = \sqrt{3}\,\textrm{.}</math>}}

-	~~This equation has the solutions~~ <math>x = \pi/3+n\pi</math> ~~for all integers ''n''.~~	+	Diese Gleichung hat die Lösungen <math>x = \pi/3+n\pi</math>

-	~~If, on the other hand,~~ <math>\cos x=0</math>, ~~then~~ <math>\sin x = \pm 1</math> (~~draw a unit circle~~) ~~and the equation cannot have such a solution.~~	+	Falls <math>\cos x=0</math>, ist <math>\sin x = \pm 1</math> (durch den Einheitskreis), und diese Gleichung hat also keine Lösung

-	~~Thus, the equation has the solutions~~	+	Also haben wir nur die Lösung

-	{{Abgesetzte Formel\|\|<math>x = \frac{\pi}{3}+n\pi\qquad</math>~~(''n'' is an arbitrary integer).~~}}	+	{{Abgesetzte Formel\|\|<math>x = \frac{\pi}{3}+n\pi\qquad</math>}}

2008-10-22T15:19:24Z

hat „Solution 4.4:8b“ nach „Lösung 4.4:8b“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 15:19, 22. Okt. 2008

2008-10-22T09:01:28Z

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

← Nächstältere Version		Version vom 09:01, 22. Okt. 2008
Zeile 1:		Zeile 1:
	Suppose that <math>\cos x\ne 0</math>, so that we can divide both sides by <math>\cos x</math> to obtain		Suppose that <math>\cos x\ne 0</math>, so that we can divide both sides by <math>\cos x</math> to obtain

-	{{~~Displayed math~~\|\|<math>\frac{\sin x}{\cos x} = \sqrt{3}\qquad\text{i.e.}\qquad \tan x = \sqrt{3}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\frac{\sin x}{\cos x} = \sqrt{3}\qquad\text{i.e.}\qquad \tan x = \sqrt{3}\,\textrm{.}</math>}}

	This equation has the solutions <math>x = \pi/3+n\pi</math> for all integers ''n''.		This equation has the solutions <math>x = \pi/3+n\pi</math> for all integers ''n''.
Zeile 9:		Zeile 9:
	Thus, the equation has the solutions		Thus, the equation has the solutions

-	{{~~Displayed math~~\|\|<math>x = \frac{\pi}{3}+n\pi\qquad</math>(''n'' is an arbitrary integer).}}	+	{{Abgesetzte Formel\|\|<math>x = \frac{\pi}{3}+n\pi\qquad</math>(''n'' is an arbitrary integer).}}

2008-10-14T08:15:34Z

← Nächstältere Version		Version vom 08:15, 14. Okt. 2008
Zeile 1:		Zeile 1:
-	Suppose that	+	Suppose that <math>\cos x\ne 0</math>, so that we can divide both sides by <math>\cos x</math> to obtain
-	<math>\~~text{~~cos }x\ne 0</math>	+
-	, so that we can divide both sides by	+
-	<math>\~~text{~~cos }x</math>	+
-	to obtain	+

-		+	{{Displayed math\|\|<math>\frac{\sin x}{\cos x} = \sqrt{3}\qquad\text{i.e.}\qquad \tan x = \sqrt{3}\,\textrm{.}</math>}}
-	<math>\frac{\sin x}{\cos x}=\sqrt{3}~~</math>~~	+
-	i.e.	+
-	~~<math>~~\tan x=\sqrt{3}</math>	+

		+	This equation has the solutions <math>x = \pi/3+n\pi</math> for all integers ''n''.

-	~~This equation has the solutions~~	+	If, on the other hand, <math>\cos x=0</math>, then <math>\sin x = \pm 1</math> (draw a unit circle) and the equation cannot have such a solution.
-	~~<math>x=\frac{\pi }{3}+n\pi </math>~~	+
-	~~for all integers~~	+
-	~~<math>n</math>.~~	+
-		+
-	If, on the other hand,	+
-	<math>\~~text{~~cos }x=0</math>, so	+
-	<math>\~~text{~~sin }x~~\text{ }~~=\pm ~~\text{~~1}</math>	+
-	( draw a unit circle) and the equation cannot have such a solution.	+

	Thus, the equation has the solutions		Thus, the equation has the solutions

-		+	{{Displayed math\|\|<math>x = \frac{\pi}{3}+n\pi\qquad</math>(''n'' is an arbitrary integer).}}
-	<math>x=\frac{\pi }{3}+n\pi </math>	+
-	(	+
-	~~<math>~~n~~</math>~~	+
-	an arbitrary integer).	+

2008-10-01T13:39:09Z

← Nächstältere Version		Version vom 13:39, 1. Okt. 2008
Zeile 1:		Zeile 1:
-	{{~~NAVCONTENT_START~~}}	+	Suppose that
-	<~~center~~> ~~[[Image:4_4_8b~~.~~gif]]~~ </~~center~~>	+	<math>\text{cos }x\ne 0</math>
-	{{~~NAVCONTENT_STOP~~}}	+	, so that we can divide both sides by
		+	<math>\text{cos }x</math>
		+	to obtain
		+
		+
		+	<math>\frac{\sin x}{\cos x}=\sqrt{3}</math>
		+	i.e.
		+	<math>\tan x=\sqrt{3}</math>
		+
		+
		+	This equation has the solutions
		+	<math>x=\frac{\pi }{3}+n\pi </math>
		+	for all integers
		+	<math>n</math>.
		+
		+	If, on the other hand,
		+	<math>\text{cos }x=0</math>, so
		+	<math>\text{sin }x\text{ }=\pm \text{1}</math>
		+	( draw a unit circle) and the equation cannot have such a solution.
		+
		+	Thus, the equation has the solutions
		+
		+
		+	<math>x=\frac{\pi }{3}+n\pi </math>
		+	(
		+	<math>n</math>
		+	an arbitrary integer).

2008-09-09T10:09:03Z

← Nächstältere Version

Version vom 10:09, 9. Sep. 2008

2008-08-21T07:21:39Z

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

2008-04-03T12:47:41Z

Ny sida: {{NAVCONTENT_START}} <center> Bild:4_4_8b.gif </center> {{NAVCONTENT_STOP}}

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