Solution 4.3:1b - Revision history

Tek at 13:03, 9 October 2008

Tek — Thu, 09 Oct 2008 13:03:22 GMT

←Older revision		Revision as of 13:03, 9 October 2008
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-	Because the sine value for an angle is equal to the angle's	+	Because the sine value for an angle is equal to the angle's ''y''-coordinate on the unit circle, two angles have the same sine value only if they have the same ''y''-coordinate. Therefore, if we draw in the angle <math>\pi/7</math> on a unit circle, we see that the only angle between <math>\pi/2</math> and <math>\pi</math> which has the same sine value lies in the second quadrant, where the line <math>y = \sin (\pi/7)</math> cuts the unit circle.
-	~~<math>~~y~~</math>~~	+
-	-coordinate on a unit circle, two angles have the same sine value only if they have the same ~~<math>~~y~~</math>~~-coordinate. Therefore, if we draw in the angle	+
-	<math>{\pi }/{7~~}\;~~</math>	+
-	on a unit circle, we see that the only angle between	+
-	<math>{\pi }/{2~~}\;~~</math>	+
-	and	+
-	<math>\pi </math>	+
-	which has the same sine value lies in the second quadrant, where the line	+
-	<math>{y=\sin \pi }/{7~~}\;~~</math>	+
-	cuts the unit circle.	+

		+	[[Image:4_3_1_b.gif\|\|center]]

-	~~<center> [[Image:4_3_1_b.gif]] </center>~~	+	Because of symmetry, we have that this angle is the reflection of the angle <math>\pi/7</math> in the ''y''-axis, i.e. <math>v = \pi - \pi/7 = 6\pi/7\,</math>.
-		+
-	~~the line~~	+
-	~~<math>{y=\sin \pi }/{7}\;</math>~~	+
-	~~the line~~	+
-	~~<math>{y=\sin \pi }/{7}\;</math>~~	+
-		+
-		+
-	Because of symmetry, we have that this angle is the reflection of the angle	+
-	<math>{\pi }/{7~~}\;~~</math>	+
-	in the	+
-	~~<math>~~y~~</math>~~-axis, i.e.	+
-		+
-	<math>v=\pi -{\pi }/{7~~}\;~~={6\pi }/{7}\;</math>.	+

Ian at 10:14, 29 September 2008

Ian — Mon, 29 Sep 2008 10:14:55 GMT

←Older revision		Revision as of 10:14, 29 September 2008
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-	~~FIGURE1 FIGURE2~~	+	<center> [[Image:4_3_1_b.gif]] </center>
-	the line	+
		+	the line
	<math>{y=\sin \pi }/{7}\;</math>		<math>{y=\sin \pi }/{7}\;</math>
-	the line	+	the line
	<math>{y=\sin \pi }/{7}\;</math>		<math>{y=\sin \pi }/{7}\;</math>

Ian at 11:59, 12 September 2008

Ian — Fri, 12 Sep 2008 11:59:23 GMT

←Older revision		Revision as of 11:59, 12 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	Because the sine value for an angle is equal to the angle's
-	<~~center~~> ~~[[Image:4_3_1_b.gif]]~~ </~~center~~>	+	<math>y</math>
		+	-coordinate on a unit circle, two angles have the same sine value only if they have the same <math>y</math>-coordinate. Therefore, if we draw in the angle
		+	<math>{\pi }/{7}\;</math>
		+	on a unit circle, we see that the only angle between
		+	<math>{\pi }/{2}\;</math>
		+	and
		+	<math>\pi </math>
		+	which has the same sine value lies in the second quadrant, where the line
		+	<math>{y=\sin \pi }/{7}\;</math>
		+	cuts the unit circle.

-	<~~center~~> ~~[[Image:4_3_1b.gif]]~~ </~~center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+	FIGURE1 FIGURE2
		+	the line
		+	<math>{y=\sin \pi }/{7}\;</math>
		+	the line
		+	<math>{y=\sin \pi }/{7}\;</math>
		+
		+
		+	Because of symmetry, we have that this angle is the reflection of the angle
		+	<math>{\pi }/{7}\;</math>
		+	in the
		+	<math>y</math>-axis, i.e.
		+
		+	<math>v=\pi -{\pi }/{7}\;={6\pi }/{7}\;</math>.

Tekbot: Lösning 4.3:1b moved to Solution 4.3:1b: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:50:43 GMT

Lösning 4.3:1b moved to Solution 4.3:1b: Robot: moved page

←Older revision

Revision as of 09:50, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 07:12:29 GMT

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

←Older revision		Revision as of 07:12, 21 August 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:4_3_1_b.gif]] </center>	+	<center> [[Image:4_3_1_b.gif]] </center>

-	<center> [[~~Bild~~:4_3_1b.gif]] </center>	+	<center> [[Image:4_3_1b.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Martin at 15:11, 15 August 2008

Martin — Fri, 15 Aug 2008 15:11:23 GMT

←Older revision		Revision as of 15:11, 15 August 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
		+	<center> [[Bild:4_3_1_b.gif]] </center>
		+
	<center> [[Bild:4_3_1b.gif]] </center>		<center> [[Bild:4_3_1b.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Oskar: Ny sida: {{NAVCONTENT_START}} Bild:4_3_1b.gif {{NAVCONTENT_STOP}}

Oskar — Thu, 03 Apr 2008 09:39:59 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:4_3_1b.gif </center> {{NAVCONTENT_STOP}}

New page

{{NAVCONTENT_START}}
<center> [[Bild:4_3_1b.gif]] </center>
{{NAVCONTENT_STOP}}