Solution 4.2:3c - Revision history

Tek at 07:53, 9 October 2008

Tek — Thu, 09 Oct 2008 07:53:18 GMT

←Older revision		Revision as of 07:53, 9 October 2008
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		+	We can add and subtract multiples of <math>2\pi</math> to or from the argument of the sine function without changing its value. The angle <math>2\pi</math> corresponds to a whole turn in a unit circle and the sine function returns to the same value every time the angle changes by a complete revolution.

-	~~We can add and subtract multiples of~~	+	For example, if we can subtract sufficiently many <math>2\pi</math>'s from <math>9\pi</math>, we will obtain a more manageable argument which lies between <math>0</math> and <math>2\pi\,</math>,
-	~~<math>\text{2}\pi </math>~~	+
-	~~to or from the argument of the sine function without changing its value. The angle~~	+
-	~~<math>\text{2}\pi </math>~~	+
-	~~corresponds to a whole turn in a unit circle and the sine function returns to the same value every time the angle changes by a complete revolution.~~	+
-		+
-	For example, if we can subtract sufficiently many	+
-	<math>~~\text{~~2}\pi </math>	+
-	s from	+
-	<math>~~\text{~~9}\pi </math>, we will obtain a more manageable argument which lies between	+
-	<math>0</math>	+
-	and	+
-	<math>~~\text{~~2}\pi ~~</math>,~~	+
-		+
-		+
-	~~<math>~~\~~text{sin 9}\pi =\text{sin}\left( 9\pi -2\pi -2\pi -2\pi -2\pi \right)=\sin \pi </math>~~	+
-		+
-		+
-	~~The line which makes an angle~~	+
-	~~<math>\pi </math>~~	+
-	~~with the positive part of the~~	+
-	~~<math>x</math>~~	+
-	~~-axis is the negative part of the~~	+
-	~~<math>x</math>~~	+
-	~~-axis~~	+
-	~~and it cuts the unit circle at the point~~	+
-	~~<math>\left( -1 \right.~~,~~\left. 0 \right)~~</math>, ~~which is why we can see from the~~	+
-	~~<math>y</math>~~	+
-	~~-coordinate that~~	+
-	~~<math>\text{sin 9}\pi =\text{sin }\pi =0</math>.~~	+

		+	{{Displayed math\|\|<math>\sin 9\pi = \sin (9\pi - 2\pi - 2\pi - 2\pi - 2\pi) = \sin \pi\,\textrm{.}</math>}}

		+	The line which makes an angle <math>\pi</math> with the positive part of the ''x''-axis is the negative part of the ''x''-axis and it cuts the unit circle at the point (-1,0), which is why we can see from the ''y''-coordinate that <math>\sin 9\pi = \sin \pi = 0\,</math>.

	[[Image:4_2_3_c.gif\|center]]		[[Image:4_2_3_c.gif\|center]]

Ian at 11:57, 28 September 2008

Ian — Sun, 28 Sep 2008 11:57:50 GMT

←Older revision		Revision as of 11:57, 28 September 2008
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-	{{~~NAVCONTENT_START~~}}	+
-	<~~center~~> ~~[[Image:4_2_3c.gif]]~~ </~~center~~>	+	We can add and subtract multiples of
-	{{~~NAVCONTENT_STOP~~}}	+	<math>\text{2}\pi </math>
		+	to or from the argument of the sine function without changing its value. The angle
		+	<math>\text{2}\pi </math>
		+	corresponds to a whole turn in a unit circle and the sine function returns to the same value every time the angle changes by a complete revolution.
		+
		+	For example, if we can subtract sufficiently many
		+	<math>\text{2}\pi </math>
		+	s from
		+	<math>\text{9}\pi </math>, we will obtain a more manageable argument which lies between
		+	<math>0</math>
		+	and
		+	<math>\text{2}\pi </math>,
		+
		+
		+	<math>\text{sin 9}\pi =\text{sin}\left( 9\pi -2\pi -2\pi -2\pi -2\pi \right)=\sin \pi </math>
		+
		+
		+	The line which makes an angle
		+	<math>\pi </math>
		+	with the positive part of the
		+	<math>x</math>
		+	-axis is the negative part of the
		+	<math>x</math>
		+	-axis
		+	and it cuts the unit circle at the point
		+	<math>\left( -1 \right.,\left. 0 \right)</math>, which is why we can see from the
		+	<math>y</math>
		+	-coordinate that
		+	<math>\text{sin 9}\pi =\text{sin }\pi =0</math>.
		+
		+
		+
	[[Image:4_2_3_c.gif\|center]]		[[Image:4_2_3_c.gif\|center]]

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

Tekbot — Tue, 09 Sep 2008 09:44:23 GMT

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

←Older revision

Revision as of 09:44, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 07:09:19 GMT

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

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Madde at 14:29, 15 August 2008

Madde — Fri, 15 Aug 2008 14:29:18 GMT

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Oskar — Thu, 03 Apr 2008 07:54:06 GMT

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