Solution 4.4:3a - Revision history

Tek at 12:49, 13 October 2008

2008-10-13T12:49:14Z

←Older revision		Revision as of 12:49, 13 October 2008
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-	The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type	+	The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type <math>\cos x = a\,</math>.
-	<math>\~~text{~~cos }x=a</math>.	+

-	In this case, we can see directly that one solution is	+	In this case, we can see directly that one solution is <math>x = \pi/6\,</math>. Using the unit circle, it follows that <math>x = 2\pi - \pi/6 = 11\pi/6\,</math> is the only other solution between <math>0</math> and <math>2\pi\,</math>.
-	<math>x={\pi }/{6}\;</math>. Using the unit circle, it follows that	+
-	<math>x=2\pi -{\pi }/{6~~}\;~~={11\pi }/{6}\;</math>	+
-	is the only other solution between	+
-	<math>0</math>	+
-	and	+
-	<math>~~\text{~~2}\pi </math>.	+

	[[Image:4_4_3_a.gif\|center]]		[[Image:4_4_3_a.gif\|center]]

-	We obtain all solutions to the equation if we add multiples of	+	We obtain all solutions to the equation if we add multiples of <math>2\pi</math> to the two solutions above,
-	<math>~~\text{~~2}\pi </math>	+
-	to the two solutions above:	+

		+	{{Displayed math\|\|<math>x = \frac{\pi}{6} + 2n\pi\qquad\text{and}\qquad x = \frac{11\pi}{6} + 2n\pi\,,</math>}}

-	~~<math>x=\frac{\pi }{6}+2n\pi </math>~~	+	where ''n'' is an arbitrary integer.
-	~~and~~	+
-	~~<math>x=\frac{11\pi }{6}+2n\pi </math>~~	+
-		+
-		+
-	where	+
-	~~<math>~~n~~</math>~~	+
-	is an arbitrary integer.	+

2008-10-01T09:37:23Z

←Older revision		Revision as of 09:37, 1 October 2008
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-	{~~{NAVCONTENT_START~~}}	+	The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type
-	<~~center~~> ~~[[Image:4_4_3a~~.~~gif]]~~ </~~center~~>	+	<math>\text{cos }x=a</math>.
-	{{~~NAVCONTENT_STOP~~}}	+
		+	In this case, we can see directly that one solution is
		+	<math>x={\pi }/{6}\;</math>. Using the unit circle, it follows that
		+	<math>x=2\pi -{\pi }/{6}\;={11\pi }/{6}\;</math>
		+	is the only other solution between
		+	<math>0</math>
		+	and
		+	<math>\text{2}\pi </math>.

	[[Image:4_4_3_a.gif\|center]]		[[Image:4_4_3_a.gif\|center]]
		+
		+	We obtain all solutions to the equation if we add multiples of
		+	<math>\text{2}\pi </math>
		+	to the two solutions above:
		+
		+
		+	<math>x=\frac{\pi }{6}+2n\pi </math>
		+	and
		+	<math>x=\frac{11\pi }{6}+2n\pi </math>
		+
		+
		+	where
		+	<math>n</math>
		+	is an arbitrary integer.

2008-09-09T10:04:03Z

←Older revision

Revision as of 10:04, 9 September 2008

2008-08-21T07:19:09Z

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2008-08-19T12:41:40Z

2008-04-03T12:30:24Z

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