Solution 4.4:3c - Revision history

Tek at 12:58, 13 October 2008

Tek — Mon, 13 Oct 2008 12:58:19 GMT

←Older revision		Revision as of 12:58, 13 October 2008
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-	If we consider the entire expression	+	If we consider the entire expression <math>x + 40^{\circ}</math> as an unknown, we have a basic trigonometric equation and can, with the aid of the unit circle, see that there are two solutions to the equation for <math>0^{\circ}\le x+40^{\circ}\le 360^{\circ}</math> namely <math>x+40^{\circ} = 65^{\circ}</math> and the symmetric solution <math>x + 40^{\circ} = 180^{\circ} - 65^{\circ} = 115^{\circ}\,</math>.
-	<math>x+~~\text{4}0~~^{\circ }</math>	+
-	as an unknown, we have a ~~fundamental~~ trigonometric equation and can, with the aid of the unit circle, see that there are two solutions to the equation for	+
-	<math>0^{\circ }\le x+~~\text{4}0~~^{\circ }\le ~~\text{36}0~~^{\circ }</math>	+
-	namely	+
-	<math>x+~~\text{4}0~~^{\circ }=~~\text{~~65}^{\circ }</math>	+
-	and the symmetric solution	+
-	<math>x+~~\text{4}0~~^{\circ }=~~\text{18}0~~^{\circ }-~~\text{~~65}^{\circ }=~~\text{~~115}^{\circ }</math>.	+
-		+

	[[Image:4_4_3_c.gif\|center]]		[[Image:4_4_3_c.gif\|center]]

-	It is then easy to set up the general solution by adding multiples of	+	It is then easy to set up the general solution by adding multiples of <math>360^{\circ}\,</math>,
-	<math>360^{\circ }</math>,	+
-		+
-		+
-	~~<math>x+\text{4}0^{\circ }=\text{65}^{\circ }+n\centerdot 360^{\circ }</math>~~	+
-	~~and~~	+
-	~~<math>x+\text{4}0^{\circ }=\text{115}^{\circ }+n\centerdot 360^{\circ }</math>~~	+
-		+

-	~~for all integers~~	+	{{Displayed math\|\|<math>x + 40^{\circ} = 65^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x + 40^{\circ} = 115^{\circ} + n\cdot 360^{\circ}</math>}}
-	<math>n</math>~~, which gives~~	+

		+	for all integers ''n'', which gives

-	<math>x=~~2\text{5}~~^{\circ }+n\~~centerdot~~ 360^{\circ }~~</math>~~	+	{{Displayed math\|\|<math>x = 25^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad x=75^{\circ} + n\cdot 360^{\circ}\,\textrm{.}</math>}}
-	~~and~~	+
-	~~<math>x=7~~\text{5}^{\circ }+n\~~centerdot~~ 360^{\circ }</math>	+

Ian at 09:50, 1 October 2008

Ian — Wed, 01 Oct 2008 09:50:43 GMT

←Older revision		Revision as of 09:50, 1 October 2008
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-	{{~~NAVCONTENT_START~~}}	+	If we consider the entire expression
-	<~~center~~> ~~[[Image:4_4_3c.gif]]~~ </~~center~~>	+	<math>x+\text{4}0^{\circ }</math>
-	{{~~NAVCONTENT_STOP~~}}	+	as an unknown, we have a fundamental trigonometric equation and can, with the aid of the unit circle, see that there are two solutions to the equation for
		+	<math>0^{\circ }\le x+\text{4}0^{\circ }\le \text{36}0^{\circ }</math>
		+	namely
		+	<math>x+\text{4}0^{\circ }=\text{65}^{\circ }</math>
		+	and the symmetric solution
		+	<math>x+\text{4}0^{\circ }=\text{18}0^{\circ }-\text{65}^{\circ }=\text{115}^{\circ }</math>.


	[[Image:4_4_3_c.gif\|center]]		[[Image:4_4_3_c.gif\|center]]
		+
		+	It is then easy to set up the general solution by adding multiples of
		+	<math>360^{\circ }</math>,
		+
		+
		+	<math>x+\text{4}0^{\circ }=\text{65}^{\circ }+n\centerdot 360^{\circ }</math>
		+	and
		+	<math>x+\text{4}0^{\circ }=\text{115}^{\circ }+n\centerdot 360^{\circ }</math>
		+
		+
		+	for all integers
		+	<math>n</math>, which gives
		+
		+
		+	<math>x=2\text{5}^{\circ }+n\centerdot 360^{\circ }</math>
		+	and
		+	<math>x=7\text{5}^{\circ }+n\centerdot 360^{\circ }</math>

Tekbot: Lösning 4.4:3c moved to Solution 4.4:3c: Robot: moved page

Tekbot — Tue, 09 Sep 2008 10:04:43 GMT

Lösning 4.4:3c moved to Solution 4.4:3c: Robot: moved page

←Older revision

Revision as of 10:04, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 07:19:29 GMT

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

←Older revision		Revision as of 07:19, 21 August 2008
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-	<center> [[~~Bild~~:4_4_3c.gif]] </center>	+	<center> [[Image:4_4_3c.gif]] </center>
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-	[[~~Bild~~:4_4_3_c.gif\|center]]	+	[[Image:4_4_3_c.gif\|center]]

Madde at 12:48, 19 August 2008

Madde — Tue, 19 Aug 2008 12:48:26 GMT

←Older revision		Revision as of 12:48, 19 August 2008
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		+	[[Bild:4_4_3_c.gif\|center]]

Oskar: Ny sida: {{NAVCONTENT_START}} Bild:4_4_3c.gif {{NAVCONTENT_STOP}}

Oskar — Thu, 03 Apr 2008 12:31:38 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:4_4_3c.gif </center> {{NAVCONTENT_STOP}}

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