Solution 4.2:8 - Revision history

Tek at 12:23, 9 October 2008

Tek — Thu, 09 Oct 2008 12:23:49 GMT

←Older revision		Revision as of 12:23, 9 October 2008
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-	We start by drawing three auxiliary triangles, and calling the three vertical sides	+	We start by drawing three auxiliary triangles, and calling the three vertical sides ''x'', ''y'' and ''z'', as shown in the figure.
-	~~<math>~~x,\ y~~</math>~~	+
-	and	+
-	~~<math>~~z~~</math>~~, as shown in the figure.	+
-		+

	[[Image:4_2_8.gif\|center]]		[[Image:4_2_8.gif\|center]]

-	Using the definition of cosine, we can work out	+	Using the definition of cosine, we can work out ''x'' and ''y'' from
-	~~<math>~~x~~\text{ }</math>~~	+
-	and	+
-	~~<math>~~y~~</math>~~	+
-	from	+
-		+
-		+
-	~~<math>x=a\cos \alpha </math>~~	+
-		+
-		+
-	~~<math>y=b\cos \beta </math>~~	+
-		+
-	~~and, for the same reason, we know that~~	+
-	~~<math>z\text{ }</math>~~	+
-	~~satisfies the relation~~	+
-		+
-		+
-	~~<math>z=l\cos \gamma </math>~~	+
-		+
-		+
-	~~In addition, we know that the lengths~~	+
-	~~<math>x,\ y</math>~~	+
-	~~and~~	+
-	~~<math>z</math>~~	+
-	~~satisfy the equality~~	+

		+	{{Displayed math\|\|<math>\begin{align}
		+	x &= a\cos \alpha\,,\\[3pt]
		+	y &= b\cos \beta\,,
		+	\end{align}</math>}}

-	~~<math>~~z~~=x-y</math>~~	+	and, for the same reason, we know that ''z'' satisfies the relation

		+	{{Displayed math\|\|<math>z=\ell\cos \gamma\,\textrm{.}</math>}}

-	If we ~~substitute in~~ the ~~expressions for~~	+	In addition, we know that the lengths ''x'', ''y'' and ''z'' satisfy the equality
-	~~<math>~~x,\ y~~</math>~~	+
-	and	+
-	~~<math>~~z~~</math>, we obtain~~ the ~~trigonometric equation~~	+

		+	{{Displayed math\|\|<math>z=x-y\,\textrm{.}</math>}}

-	~~<math>l\cos \gamma =a\cos \alpha -b\cos \beta </math>~~	+	If we substitute in the expressions for ''x'', ''y'' and ''z'', we obtain the trigonometric equation

		+	{{Displayed math\|\|<math>\ell\cos \gamma = a\cos \alpha -b\cos \beta\,\textrm{,}</math>}}

-	where	+	where <math>\gamma </math> is the only unknown.
-	<math>\gamma </math>	+
-	is the only unknown.	+

Ian at 09:40, 29 September 2008

Ian — Mon, 29 Sep 2008 09:40:28 GMT

←Older revision		Revision as of 09:40, 29 September 2008
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-	~~{{NAVCONTENT_START}}~~	+	We start by drawing three auxiliary triangles, and calling the three vertical sides
-	<~~center~~> ~~[[Image:4_2_8-1(2).gif]]~~ </~~center~~>	+	<math>x,\ y</math>
-	~~{{NAVCONTENT_STOP}}~~	+	and
-	~~{{NAVCONTENT_START}}~~	+	<math>z</math>, as shown in the figure.
-	<~~center~~> ~~[[Image:4_2_8-2(2).gif]]~~ </~~center~~>	+
-	~~{{NAVCONTENT_STOP}}~~	+


	[[Image:4_2_8.gif\|center]]		[[Image:4_2_8.gif\|center]]
		+
		+	Using the definition of cosine, we can work out
		+	<math>x\text{ }</math>
		+	and
		+	<math>y</math>
		+	from
		+
		+
		+	<math>x=a\cos \alpha </math>
		+
		+
		+	<math>y=b\cos \beta </math>
		+
		+	and, for the same reason, we know that
		+	<math>z\text{ }</math>
		+	satisfies the relation
		+
		+
		+	<math>z=l\cos \gamma </math>
		+
		+
		+	In addition, we know that the lengths
		+	<math>x,\ y</math>
		+	and
		+	<math>z</math>
		+	satisfy the equality
		+
		+
		+	<math>z=x-y</math>
		+
		+
		+	If we substitute in the expressions for
		+	<math>x,\ y</math>
		+	and
		+	<math>z</math>, we obtain the trigonometric equation
		+
		+
		+	<math>l\cos \gamma =a\cos \alpha -b\cos \beta </math>
		+
		+
		+	where
		+	<math>\gamma </math>
		+	is the only unknown.

Tekbot: Lösning 4.2:8 moved to Solution 4.2:8: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:49:43 GMT

Lösning 4.2:8 moved to Solution 4.2:8: Robot: moved page

←Older revision

Revision as of 09:49, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 07:11:59 GMT

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

←Older revision		Revision as of 07:11, 21 August 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:4_2_8-1(2).gif]] </center>	+	<center> [[Image:4_2_8-1(2).gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:4_2_8-2(2).gif]] </center>	+	<center> [[Image:4_2_8-2(2).gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}


-	[[~~Bild~~:4_2_8.gif\|center]]	+	[[Image:4_2_8.gif\|center]]

Madde at 14:04, 18 August 2008

Madde — Mon, 18 Aug 2008 14:04:20 GMT

←Older revision		Revision as of 14:04, 18 August 2008
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	<center> [[Bild:4_2_8-2(2).gif]] </center>		<center> [[Bild:4_2_8-2(2).gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}
		+
		+
		+	[[Bild:4_2_8.gif\|center]]

Oskar: Ny sida: {{NAVCONTENT_START}} Bild:4_2_8-1(2).gif {{NAVCONTENT_STOP}} {{NAVCONTENT_START}} Bild:4_2_8-2(2).gif {{NAVCONTENT_STOP}}

Oskar — Thu, 03 Apr 2008 08:09:10 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:4_2_8-1(2).gif </center> {{NAVCONTENT_STOP}} {{NAVCONTENT_START}} <center> Bild:4_2_8-2(2).gif </center> {{NAVCONTENT_STOP}}

New page

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