Solution 4.1:2 - Revision history

Tek at 07:59, 3 October 2008

Tek — Fri, 03 Oct 2008 07:59:19 GMT

←Older revision		Revision as of 07:59, 3 October 2008
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-	If we use the mnemonic that one turn is	+	If we use the mnemonic that one turn is 360° or <math>2\pi</math> radians, we can derive a formula for the transformation from degrees to radians. Because
-	~~<math>360^{\circ }</math>~~	+
-	or	+
-	<math>~~\text{~~2}\pi </math>	+
-	radians, we can derive a formula for the transformation from degrees to radians. Because	+

-		+	{{Displayed math\|\|<math>360\cdot 1^{\circ } = 2\pi\ \text{radians}</math>}}
-	<math>360^{\~~circ }\centerdot~~ 1^{\circ }=2\pi </math>	+
-	~~radians~~	+

	this gives		this gives

-		+	{{Displayed math\|\|<math>1^{\circ} = \frac{2\pi}{360}\ \text{radians} = \frac{\pi}{180}\ \text{radians.}</math>}}
-	<math>1^{\circ }=\frac{2\pi }{360}~~</math>~~	+
-	radians	+
-	~~<math>~~=\frac{\pi }{180}</math>	+
-	~~radians~~	+

	Now we can start transforming the angles:		Now we can start transforming the angles:

-	a)
-	<math>45^{\circ }=45\centerdot 1^{\circ }=45\centerdot \frac{\pi }{180}</math>
-	radians
-	<math>=\frac{\pi }{4}</math>
-	radians
-
-	b)
-	<math>135^{\circ }=135\centerdot 1^{\circ }=135\centerdot \frac{\pi }{180}</math>
-	radians
-	<math>=\frac{3\pi }{4}</math>
-	radians
-
-	c)
-	<math>-63^{\circ }=-63\centerdot 1^{\circ }=-63\centerdot \frac{\pi }{180}</math>
-	radians
-	<math>=-\frac{7\pi }{20}</math>
-	radians

-	d)	+	{\|
-	<math>~~270~~^{\circ }=~~270~~\~~centerdot~~ 1^{\circ }=~~270~~\~~centerdot~~ \frac{\pi }{180}</math>	+	\|\|a)
-	radians	+	\|width="100%"\|<math>45^{\circ} = 45\cdot 1^{\circ} = 45\cdot\frac{\pi}{180}\ \text{radians} = \frac{\pi}{4}\ \text{radians,}</math>
-	<math>=\frac{3\pi }{2}</math>	+	\|-
-	~~radians~~	+	\|height="10px"\|
		+	\|-
		+	\|\|b)
		+	\|width="100%"\|<math>135^{\circ } = 135\cdot 1^{\circ} = 135\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}</math>
		+	\|-
		+	\|height="10px"\|
		+	\|-
		+	\|\|c)
		+	\|width="100%"\|<math>-63^{\circ} = -63\cdot 1^{\circ} = -63\cdot\frac{\pi}{180}\ \text{radians} = -\frac{7\pi}{20}\ \text{radians,}</math>
		+	\|-
		+	\|height="10px"\|
		+	\|-
		+	\|\|d)
		+	\|width="100%"\|<math>270^{\circ} = 270\cdot 1^{\circ} = 270\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{2}\ \text{radians.}</math>
		+	\|}

Ian at 09:17, 27 September 2008

Ian — Sat, 27 Sep 2008 09:17:25 GMT

←Older revision		Revision as of 09:17, 27 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	If we use the mnemonic that one turn is
-	<~~center~~> ~~[[Image~~:~~4_1_2.gif]]~~ </~~center~~>	+	<math>360^{\circ }</math>
-	{{~~NAVCONTENT_STOP~~}}	+	or
		+	<math>\text{2}\pi </math>
		+	radians, we can derive a formula for the transformation from degrees to radians. Because
		+
		+
		+	<math>360^{\circ }\centerdot 1^{\circ }=2\pi </math>
		+	radians
		+
		+	this gives
		+
		+
		+	<math>1^{\circ }=\frac{2\pi }{360}</math>
		+	radians
		+	<math>=\frac{\pi }{180}</math>
		+	radians
		+
		+	Now we can start transforming the angles:
		+
		+	a)
		+	<math>45^{\circ }=45\centerdot 1^{\circ }=45\centerdot \frac{\pi }{180}</math>
		+	radians
		+	<math>=\frac{\pi }{4}</math>
		+	radians
		+
		+	b)
		+	<math>135^{\circ }=135\centerdot 1^{\circ }=135\centerdot \frac{\pi }{180}</math>
		+	radians
		+	<math>=\frac{3\pi }{4}</math>
		+	radians
		+
		+	c)
		+	<math>-63^{\circ }=-63\centerdot 1^{\circ }=-63\centerdot \frac{\pi }{180}</math>
		+	radians
		+	<math>=-\frac{7\pi }{20}</math>
		+	radians
		+
		+	d)
		+	<math>270^{\circ }=270\centerdot 1^{\circ }=270\centerdot \frac{\pi }{180}</math>
		+	radians
		+	<math>=\frac{3\pi }{2}</math>
		+	radians

Tekbot: Lösning 4.1:2 moved to Solution 4.1:2: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:33:43 GMT

Lösning 4.1:2 moved to Solution 4.1:2: Robot: moved page

←Older revision

Revision as of 09:33, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 07:03:59 GMT

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

←Older revision		Revision as of 07:03, 21 August 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:4_1_2.gif]] </center>	+	<center> [[Image:4_1_2.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Oskar: Ny sida: {{NAVCONTENT_START}} Bild:4_1_2.gif {{NAVCONTENT_STOP}}

Oskar — Wed, 02 Apr 2008 12:52:47 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:4_1_2.gif </center> {{NAVCONTENT_STOP}}

New page

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