4.3 Exercises - Revision history

Tekbot: Robot: Automated text replacement (-{{Vald flik +{{Selected tab)

2008-09-10T13:52:25Z

Robot: Automated text replacement (-{{Vald flik +{{Selected tab)

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	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
	{{Not selected tab\|[[4.3 Trigonometric relations\|Theory]]}}		{{Not selected tab\|[[4.3 Trigonometric relations\|Theory]]}}
-	{{~~Vald flik~~\|[[4.3 Exercises\|Exercises]]}}	+	{{Selected tab\|[[4.3 Exercises\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|
	\|}		\|}

Tekbot: Robot: Automated text replacement (-{{Ej vald flik +{{Not selected tab)

2008-09-10T13:47:02Z

Robot: Automated text replacement (-{{Ej vald flik +{{Not selected tab)

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	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
-	{{~~Ej vald flik~~\|[[4.3 Trigonometric relations\|Theory]]}}	+	{{Not selected tab\|[[4.3 Trigonometric relations\|Theory]]}}
	{{Vald flik\|[[4.3 Exercises\|Exercises]]}}		{{Vald flik\|[[4.3 Exercises\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|

Tekbot: Robot: Automated text replacement (-4.3 Trigonometriska samband +4.3 Trigonometric relations)

2008-09-10T13:38:58Z

Robot: Automated text replacement (-4.3 Trigonometriska samband +4.3 Trigonometric relations)

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	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
-	{{Ej vald flik\|[[4.3 ~~Trigonometriska samband~~\|Theory]]}}	+	{{Ej vald flik\|[[4.3 Trigonometric relations\|Theory]]}}
	{{Vald flik\|[[4.3 Exercises\|Exercises]]}}		{{Vald flik\|[[4.3 Exercises\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|

Tekbot: Robot: Automated text replacement (-Övningar +Exercises)

2008-09-10T10:49:12Z

Robot: Automated text replacement (-Övningar +Exercises)

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	{{Ej vald flik\|[[4.3 Trigonometriska samband\|Theory]]}}		{{Ej vald flik\|[[4.3 Trigonometriska samband\|Theory]]}}
-	{{Vald flik\|[[4.3 ~~Övningar~~\|Exercises]]}}	+	{{Vald flik\|[[4.3 Exercises\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|
	\|}		\|}

Tekbot: 4.3 Övningar moved to 4.3 Exercises: Robot: moved page

2008-09-10T10:34:56Z

4.3 Övningar moved to 4.3 Exercises: Robot: moved page

←Older revision

Revision as of 10:34, 10 September 2008

Tekbot: Robot: Automated text replacement (-Lösning +Solution)

2008-09-09T11:22:19Z

Robot: Automated text replacement (-Lösning +Solution)

←Older revision		Revision as of 11:22, 9 September 2008
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	\|width="33%" \| <math>\tan{v}=\tan{\displaystyle \frac{2\pi}{7}}</math>		\|width="33%" \| <math>\tan{v}=\tan{\displaystyle \frac{2\pi}{7}}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|Answer 4.3:1\|Solution a \|~~Lösning~~ 4.3:1a\|Solution b \|~~Lösning~~ 4.3:1b\|Solution c \|~~Lösning~~ 4.3:1c}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:1\|Solution a \|Solution 4.3:1a\|Solution b \|Solution 4.3:1b\|Solution c \|Solution 4.3:1c}}

	===Exercise 4.3:2===		===Exercise 4.3:2===
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	\|width="50%" \| <math>\cos{v} = \cos{ \displaystyle \frac{7\pi}{5}}</math>		\|width="50%" \| <math>\cos{v} = \cos{ \displaystyle \frac{7\pi}{5}}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|Answer 4.3:2\|Solution a \|~~Lösning~~ 4.3:2a\|Solution b \|~~Lösning~~ 4.3:2b}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:2\|Solution a \|Solution 4.3:2a\|Solution b \|Solution 4.3:2b}}

	===Exercise 4.3:3===		===Exercise 4.3:3===
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	\|width="50%" \| <math>\sin{\left( \displaystyle \frac{\pi}{3} + v \right)}</math>		\|width="50%" \| <math>\sin{\left( \displaystyle \frac{\pi}{3} + v \right)}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|Answer 4.3:3\|Solution a \|~~Lösning~~ 4.3:3a\|Solution b \|~~Lösning~~ 4.3:3b\|Solution c \|~~Lösning~~ 4.3:3c\|Solution d \|~~Lösning~~ 4.3:3d\|Solution e \|~~Lösning~~ 4.3:3e\|Solution f \|~~Lösning~~ 4.3:3f}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:3\|Solution a \|Solution 4.3:3a\|Solution b \|Solution 4.3:3b\|Solution c \|Solution 4.3:3c\|Solution d \|Solution 4.3:3d\|Solution e \|Solution 4.3:3e\|Solution f \|Solution 4.3:3f}}

	===Exercise 4.3:4===		===Exercise 4.3:4===
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	\|width="50%" \| <math>\cos{\left( v-\displaystyle \frac{\pi}{3} \right)}</math>		\|width="50%" \| <math>\cos{\left( v-\displaystyle \frac{\pi}{3} \right)}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|Answer 4.3:4\|Solution a \|~~Lösning~~ 4.3:4a\|Solution b \|~~Lösning~~ 4.3:4b\|Solution c \|~~Lösning~~ 4.3:4c\|Solution d \|~~Lösning~~ 4.3:4d\|Solution e \|~~Lösning~~ 4.3:4e\|Solution f \|~~Lösning~~ 4.3:4f}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:4\|Solution a \|Solution 4.3:4a\|Solution b \|Solution 4.3:4b\|Solution c \|Solution 4.3:4c\|Solution d \|Solution 4.3:4d\|Solution e \|Solution 4.3:4e\|Solution f \|Solution 4.3:4f}}

	===Exercise 4.3:5===		===Exercise 4.3:5===
	<div class="ovning">		<div class="ovning">
	Determine <math>\,\cos{v}\,</math> and <math>\,\tan{v}\,</math>, where <math>\,v\,</math> is an acute angle in a triangle such that <math>\,\sin{v}=\displaystyle \frac{5}{7}\,</math>.		Determine <math>\,\cos{v}\,</math> and <math>\,\tan{v}\,</math>, where <math>\,v\,</math> is an acute angle in a triangle such that <math>\,\sin{v}=\displaystyle \frac{5}{7}\,</math>.
-	</div>{{#NAVCONTENT:Answer\|Answer 4.3:5\|Solution \|~~Lösning~~ 4.3:5}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:5\|Solution \|Solution 4.3:5}}

	===Exercise 4.3:6===		===Exercise 4.3:6===
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	\|width="100%" \| Determine <math>\ \sin{v}\ </math> and <math>\ \cos{v}\ </math> if <math>\ \tan{v}=3\ </math> and <math>\ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,</math>.		\|width="100%" \| Determine <math>\ \sin{v}\ </math> and <math>\ \cos{v}\ </math> if <math>\ \tan{v}=3\ </math> and <math>\ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,</math>.
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|Answer 4.3:6\|Solution a \|~~Lösning~~ 4.3:6a\|Solution b \|~~Lösning~~ 4.3:6b\|Solution c \|~~Lösning~~ 4.3:6c}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:6\|Solution a \|Solution 4.3:6a\|Solution b \|Solution 4.3:6b\|Solution c \|Solution 4.3:6c}}

	===Exercise 4.3:7===		===Exercise 4.3:7===
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	\|width="100%" \| <math>\cos{x}=\displaystyle \frac{2}{5}\,</math>, <math>\ \cos{y}=\displaystyle \frac{3}{5}\ </math> and <math>\,x\,</math>, <math>\,y\,</math> are angles in the first quadrant.		\|width="100%" \| <math>\cos{x}=\displaystyle \frac{2}{5}\,</math>, <math>\ \cos{y}=\displaystyle \frac{3}{5}\ </math> and <math>\,x\,</math>, <math>\,y\,</math> are angles in the first quadrant.
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|Answer 4.3:7\|Solution a \|~~Lösning~~ 4.3:7a\|Solution b \|~~Lösning~~ 4.3:7b}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:7\|Solution a \|Solution 4.3:7a\|Solution b \|Solution 4.3:7b}}

	===Exercise 4.3:8===		===Exercise 4.3:8===
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	\|width="100%" \| <math>\displaystyle\frac{\cos (u+v)}{\cos u \cos v}= 1- \tan u \tan v</math>		\|width="100%" \| <math>\displaystyle\frac{\cos (u+v)}{\cos u \cos v}= 1- \tan u \tan v</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Solution a \|~~Lösning~~ 4.3:8a\|Solution b \|~~Lösning~~ 4.3:8b\|Solution c \|~~Lösning~~ 4.3:8c\|Solution d \|~~Lösning~~ 4.3:8d}}	+	</div>{{#NAVCONTENT:Solution a \|Solution 4.3:8a\|Solution b \|Solution 4.3:8b\|Solution c \|Solution 4.3:8c\|Solution d \|Solution 4.3:8d}}

	===Exercise 4.3:9===		===Exercise 4.3:9===
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	\|width="100%" \|(Hint: use the formula for double angles on <math>\,\sin 160^\circ\,</math>.)		\|width="100%" \|(Hint: use the formula for double angles on <math>\,\sin 160^\circ\,</math>.)
	\|}		\|}
-	</div>{{#NAVCONTENT:Solution \|~~Lösning~~ 4.3:9}}	+	</div>{{#NAVCONTENT:Solution \|Solution 4.3:9}}

Tekbot: Robot: Automated text replacement (-Svar +Answer)

2008-09-09T07:11:22Z

Robot: Automated text replacement (-Svar +Answer)

←Older revision		Revision as of 07:11, 9 September 2008
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	\|width="33%" \| <math>\tan{v}=\tan{\displaystyle \frac{2\pi}{7}}</math>		\|width="33%" \| <math>\tan{v}=\tan{\displaystyle \frac{2\pi}{7}}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|~~Svar~~ 4.3:1\|Solution a \|Lösning 4.3:1a\|Solution b \|Lösning 4.3:1b\|Solution c \|Lösning 4.3:1c}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:1\|Solution a \|Lösning 4.3:1a\|Solution b \|Lösning 4.3:1b\|Solution c \|Lösning 4.3:1c}}

	===Exercise 4.3:2===		===Exercise 4.3:2===
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	\|width="50%" \| <math>\cos{v} = \cos{ \displaystyle \frac{7\pi}{5}}</math>		\|width="50%" \| <math>\cos{v} = \cos{ \displaystyle \frac{7\pi}{5}}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|~~Svar~~ 4.3:2\|Solution a \|Lösning 4.3:2a\|Solution b \|Lösning 4.3:2b}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:2\|Solution a \|Lösning 4.3:2a\|Solution b \|Lösning 4.3:2b}}

	===Exercise 4.3:3===		===Exercise 4.3:3===
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	\|width="50%" \| <math>\sin{\left( \displaystyle \frac{\pi}{3} + v \right)}</math>		\|width="50%" \| <math>\sin{\left( \displaystyle \frac{\pi}{3} + v \right)}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|~~Svar~~ 4.3:3\|Solution a \|Lösning 4.3:3a\|Solution b \|Lösning 4.3:3b\|Solution c \|Lösning 4.3:3c\|Solution d \|Lösning 4.3:3d\|Solution e \|Lösning 4.3:3e\|Solution f \|Lösning 4.3:3f}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:3\|Solution a \|Lösning 4.3:3a\|Solution b \|Lösning 4.3:3b\|Solution c \|Lösning 4.3:3c\|Solution d \|Lösning 4.3:3d\|Solution e \|Lösning 4.3:3e\|Solution f \|Lösning 4.3:3f}}

	===Exercise 4.3:4===		===Exercise 4.3:4===
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	\|width="50%" \| <math>\cos{\left( v-\displaystyle \frac{\pi}{3} \right)}</math>		\|width="50%" \| <math>\cos{\left( v-\displaystyle \frac{\pi}{3} \right)}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|~~Svar~~ 4.3:4\|Solution a \|Lösning 4.3:4a\|Solution b \|Lösning 4.3:4b\|Solution c \|Lösning 4.3:4c\|Solution d \|Lösning 4.3:4d\|Solution e \|Lösning 4.3:4e\|Solution f \|Lösning 4.3:4f}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:4\|Solution a \|Lösning 4.3:4a\|Solution b \|Lösning 4.3:4b\|Solution c \|Lösning 4.3:4c\|Solution d \|Lösning 4.3:4d\|Solution e \|Lösning 4.3:4e\|Solution f \|Lösning 4.3:4f}}

	===Exercise 4.3:5===		===Exercise 4.3:5===
	<div class="ovning">		<div class="ovning">
	Determine <math>\,\cos{v}\,</math> and <math>\,\tan{v}\,</math>, where <math>\,v\,</math> is an acute angle in a triangle such that <math>\,\sin{v}=\displaystyle \frac{5}{7}\,</math>.		Determine <math>\,\cos{v}\,</math> and <math>\,\tan{v}\,</math>, where <math>\,v\,</math> is an acute angle in a triangle such that <math>\,\sin{v}=\displaystyle \frac{5}{7}\,</math>.
-	</div>{{#NAVCONTENT:Answer\|~~Svar~~ 4.3:5\|Solution \|Lösning 4.3:5}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:5\|Solution \|Lösning 4.3:5}}

	===Exercise 4.3:6===		===Exercise 4.3:6===
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	\|width="100%" \| Determine <math>\ \sin{v}\ </math> and <math>\ \cos{v}\ </math> if <math>\ \tan{v}=3\ </math> and <math>\ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,</math>.		\|width="100%" \| Determine <math>\ \sin{v}\ </math> and <math>\ \cos{v}\ </math> if <math>\ \tan{v}=3\ </math> and <math>\ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,</math>.
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|~~Svar~~ 4.3:6\|Solution a \|Lösning 4.3:6a\|Solution b \|Lösning 4.3:6b\|Solution c \|Lösning 4.3:6c}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:6\|Solution a \|Lösning 4.3:6a\|Solution b \|Lösning 4.3:6b\|Solution c \|Lösning 4.3:6c}}

	===Exercise 4.3:7===		===Exercise 4.3:7===
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	\|width="100%" \| <math>\cos{x}=\displaystyle \frac{2}{5}\,</math>, <math>\ \cos{y}=\displaystyle \frac{3}{5}\ </math> and <math>\,x\,</math>, <math>\,y\,</math> are angles in the first quadrant.		\|width="100%" \| <math>\cos{x}=\displaystyle \frac{2}{5}\,</math>, <math>\ \cos{y}=\displaystyle \frac{3}{5}\ </math> and <math>\,x\,</math>, <math>\,y\,</math> are angles in the first quadrant.
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|~~Svar~~ 4.3:7\|Solution a \|Lösning 4.3:7a\|Solution b \|Lösning 4.3:7b}}	+	</div>{{#NAVCONTENT:Answer\|Answer 4.3:7\|Solution a \|Lösning 4.3:7a\|Solution b \|Lösning 4.3:7b}}

	===Exercise 4.3:8===		===Exercise 4.3:8===

Tek: Translated links into English

2008-08-19T14:43:07Z

Translated links into English

←Older revision		Revision as of 14:43, 19 August 2008
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	\|width="33%" \| <math>\tan{v}=\tan{\displaystyle \frac{2\pi}{7}}</math>		\|width="33%" \| <math>\tan{v}=\tan{\displaystyle \frac{2\pi}{7}}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:~~Svar~~\|Svar 4.3:1\|~~Lösning~~ a \|Lösning 4.3:1a\|~~Lösning~~ b \|Lösning 4.3:1b\|~~Lösning~~ c \|Lösning 4.3:1c}}	+	</div>{{#NAVCONTENT:Answer\|Svar 4.3:1\|Solution a \|Lösning 4.3:1a\|Solution b \|Lösning 4.3:1b\|Solution c \|Lösning 4.3:1c}}

	===Exercise 4.3:2===		===Exercise 4.3:2===
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	\|width="50%" \| <math>\cos{v} = \cos{ \displaystyle \frac{7\pi}{5}}</math>		\|width="50%" \| <math>\cos{v} = \cos{ \displaystyle \frac{7\pi}{5}}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:~~Svar~~\|Svar 4.3:2\|~~Lösning~~ a \|Lösning 4.3:2a\|~~Lösning~~ b \|Lösning 4.3:2b}}	+	</div>{{#NAVCONTENT:Answer\|Svar 4.3:2\|Solution a \|Lösning 4.3:2a\|Solution b \|Lösning 4.3:2b}}

	===Exercise 4.3:3===		===Exercise 4.3:3===
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	\|width="50%" \| <math>\sin{\left( \displaystyle \frac{\pi}{3} + v \right)}</math>		\|width="50%" \| <math>\sin{\left( \displaystyle \frac{\pi}{3} + v \right)}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:~~Svar~~\|Svar 4.3:3\|~~Lösning~~ a \|Lösning 4.3:3a\|~~Lösning~~ b \|Lösning 4.3:3b\|~~Lösning~~ c \|Lösning 4.3:3c\|~~Lösning~~ d \|Lösning 4.3:3d\|~~Lösning~~ e \|Lösning 4.3:3e\|~~Lösning~~ f \|Lösning 4.3:3f}}	+	</div>{{#NAVCONTENT:Answer\|Svar 4.3:3\|Solution a \|Lösning 4.3:3a\|Solution b \|Lösning 4.3:3b\|Solution c \|Lösning 4.3:3c\|Solution d \|Lösning 4.3:3d\|Solution e \|Lösning 4.3:3e\|Solution f \|Lösning 4.3:3f}}

	===Exercise 4.3:4===		===Exercise 4.3:4===
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	\|width="50%" \| <math>\cos{\left( v-\displaystyle \frac{\pi}{3} \right)}</math>		\|width="50%" \| <math>\cos{\left( v-\displaystyle \frac{\pi}{3} \right)}</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:~~Svar~~\|Svar 4.3:4\|~~Lösning~~ a \|Lösning 4.3:4a\|~~Lösning~~ b \|Lösning 4.3:4b\|~~Lösning~~ c \|Lösning 4.3:4c\|~~Lösning~~ d \|Lösning 4.3:4d\|~~Lösning~~ e \|Lösning 4.3:4e\|~~Lösning~~ f \|Lösning 4.3:4f}}	+	</div>{{#NAVCONTENT:Answer\|Svar 4.3:4\|Solution a \|Lösning 4.3:4a\|Solution b \|Lösning 4.3:4b\|Solution c \|Lösning 4.3:4c\|Solution d \|Lösning 4.3:4d\|Solution e \|Lösning 4.3:4e\|Solution f \|Lösning 4.3:4f}}

	===Exercise 4.3:5===		===Exercise 4.3:5===
	<div class="ovning">		<div class="ovning">
	Determine <math>\,\cos{v}\,</math> and <math>\,\tan{v}\,</math>, where <math>\,v\,</math> is an acute angle in a triangle such that <math>\,\sin{v}=\displaystyle \frac{5}{7}\,</math>.		Determine <math>\,\cos{v}\,</math> and <math>\,\tan{v}\,</math>, where <math>\,v\,</math> is an acute angle in a triangle such that <math>\,\sin{v}=\displaystyle \frac{5}{7}\,</math>.
-	</div>{{#NAVCONTENT:~~Svar~~\|Svar 4.3:5\|~~Lösning~~ \|Lösning 4.3:5}}	+	</div>{{#NAVCONTENT:Answer\|Svar 4.3:5\|Solution \|Lösning 4.3:5}}

	===Exercise 4.3:6===		===Exercise 4.3:6===
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	\|width="100%" \| Determine <math>\ \sin{v}\ </math> and <math>\ \cos{v}\ </math> if <math>\ \tan{v}=3\ </math> and <math>\ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,</math>.		\|width="100%" \| Determine <math>\ \sin{v}\ </math> and <math>\ \cos{v}\ </math> if <math>\ \tan{v}=3\ </math> and <math>\ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,</math>.
	\|}		\|}
-	</div>{{#NAVCONTENT:~~Svar~~\|Svar 4.3:6\|~~Lösning~~ a \|Lösning 4.3:6a\|~~Lösning~~ b \|Lösning 4.3:6b\|~~Lösning~~ c \|Lösning 4.3:6c}}	+	</div>{{#NAVCONTENT:Answer\|Svar 4.3:6\|Solution a \|Lösning 4.3:6a\|Solution b \|Lösning 4.3:6b\|Solution c \|Lösning 4.3:6c}}

	===Exercise 4.3:7===		===Exercise 4.3:7===
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	\|width="100%" \| <math>\cos{x}=\displaystyle \frac{2}{5}\,</math>, <math>\ \cos{y}=\displaystyle \frac{3}{5}\ </math> and <math>\,x\,</math>, <math>\,y\,</math> are angles in the first quadrant.		\|width="100%" \| <math>\cos{x}=\displaystyle \frac{2}{5}\,</math>, <math>\ \cos{y}=\displaystyle \frac{3}{5}\ </math> and <math>\,x\,</math>, <math>\,y\,</math> are angles in the first quadrant.
	\|}		\|}
-	</div>{{#NAVCONTENT:~~Svar~~\|Svar 4.3:7\|~~Lösning~~ a \|Lösning 4.3:7a\|~~Lösning~~ b \|Lösning 4.3:7b}}	+	</div>{{#NAVCONTENT:Answer\|Svar 4.3:7\|Solution a \|Lösning 4.3:7a\|Solution b \|Lösning 4.3:7b}}

	===Exercise 4.3:8===		===Exercise 4.3:8===
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	\|width="100%" \| <math>\displaystyle\frac{\cos (u+v)}{\cos u \cos v}= 1- \tan u \tan v</math>		\|width="100%" \| <math>\displaystyle\frac{\cos (u+v)}{\cos u \cos v}= 1- \tan u \tan v</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:~~Lösning~~ a \|Lösning 4.3:8a\|~~Lösning~~ b \|Lösning 4.3:8b\|~~Lösning~~ c \|Lösning 4.3:8c\|~~Lösning~~ d \|Lösning 4.3:8d}}	+	</div>{{#NAVCONTENT:Solution a \|Lösning 4.3:8a\|Solution b \|Lösning 4.3:8b\|Solution c \|Lösning 4.3:8c\|Solution d \|Lösning 4.3:8d}}

	===Exercise 4.3:9===		===Exercise 4.3:9===
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	\|width="100%" \|(Hint: use the formula for double angles on <math>\,\sin 160^\circ\,</math>.)		\|width="100%" \|(Hint: use the formula for double angles on <math>\,\sin 160^\circ\,</math>.)
	\|}		\|}
-	</div>{{#NAVCONTENT:~~Lösning~~ \|Lösning 4.3:9}}	+	</div>{{#NAVCONTENT:Solution \|Lösning 4.3:9}}

Ian at 18:14, 3 August 2008

2008-08-03T18:14:36Z

←Older revision		Revision as of 18:14, 3 August 2008
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	{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"		{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
-	{{Ej vald flik\|[[4.3 Trigonometriska samband\|~~Teori~~]]}}	+	{{Ej vald flik\|[[4.3 Trigonometriska samband\|Theory]]}}
-	{{Vald flik\|[[4.3 Övningar\|~~Övningar~~]]}}	+	{{Vald flik\|[[4.3 Övningar\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|
	\|}		\|}

-	===~~Övning~~ 4.3:1===	+	===Exercise 4.3:1===
	<div class="ovning">		<div class="ovning">
-	~~Bestäm de vinklar~~ <math>\,v\,</math> ~~mellan~~ <math>\,\displaystyle \frac{\pi}{2}\,</math> ~~och~~ <math>\,2\pi\,</math> ~~som uppfyller~~	+	Determine the angles <math>\,v\,</math> between <math>\,\displaystyle \frac{\pi}{2}\,</math> and <math>\,2\pi\,</math> which satisfy
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
Line 20:		Line 20:
	</div>{{#NAVCONTENT:Svar\|Svar 4.3:1\|Lösning a \|Lösning 4.3:1a\|Lösning b \|Lösning 4.3:1b\|Lösning c \|Lösning 4.3:1c}}		</div>{{#NAVCONTENT:Svar\|Svar 4.3:1\|Lösning a \|Lösning 4.3:1a\|Lösning b \|Lösning 4.3:1b\|Lösning c \|Lösning 4.3:1c}}

-	===~~Övning~~ 4.3:2===	+	===Exercise 4.3:2===
	<div class="ovning">		<div class="ovning">
-	~~Bestäm de vinklar~~ <math>\,v\,</math> ~~mellan~~ 0 ~~och~~ <math>\,\pi\,</math> ~~som uppfyller~~	+	Determine the angles <math>\,v\,</math> between 0 and <math>\,\pi\,</math> which satisfy
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
Line 31:		Line 31:
	</div>{{#NAVCONTENT:Svar\|Svar 4.3:2\|Lösning a \|Lösning 4.3:2a\|Lösning b \|Lösning 4.3:2b}}		</div>{{#NAVCONTENT:Svar\|Svar 4.3:2\|Lösning a \|Lösning 4.3:2a\|Lösning b \|Lösning 4.3:2b}}

-	===~~Övning~~ 4.3:3===	+	===Exercise 4.3:3===
	<div class="ovning">		<div class="ovning">
-	~~Antag att~~ <math>\,-\displaystyle \frac{\pi}{2} \leq v \leq \displaystyle \frac{\pi}{2}\,</math> ~~och att~~ <math>\,\sin{v} = a\,</math>. ~~Uttryck med hjälp av~~ <math>\,a</math>	+	Suppose that <math>\,-\displaystyle \frac{\pi}{2} \leq v \leq \displaystyle \frac{\pi}{2}\,</math> and that <math>\,\sin{v} = a\,</math>. With the help of <math>\,a</math> express
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
Line 52:		Line 52:
	</div>{{#NAVCONTENT:Svar\|Svar 4.3:3\|Lösning a \|Lösning 4.3:3a\|Lösning b \|Lösning 4.3:3b\|Lösning c \|Lösning 4.3:3c\|Lösning d \|Lösning 4.3:3d\|Lösning e \|Lösning 4.3:3e\|Lösning f \|Lösning 4.3:3f}}		</div>{{#NAVCONTENT:Svar\|Svar 4.3:3\|Lösning a \|Lösning 4.3:3a\|Lösning b \|Lösning 4.3:3b\|Lösning c \|Lösning 4.3:3c\|Lösning d \|Lösning 4.3:3d\|Lösning e \|Lösning 4.3:3e\|Lösning f \|Lösning 4.3:3f}}

-	===~~Övning~~ 4.3:4===	+	===Exercise 4.3:4===
	<div class="ovning">		<div class="ovning">
-	~~Antag att~~ <math>\,0 \leq v \leq \pi\,</math> ~~och att~~ <math>\,\cos{v}=b\,</math>. ~~Uttryck med hjälp av~~ <math>\,b</math>	+	Suppose that <math>\,0 \leq v \leq \pi\,</math> and that <math>\,\cos{v}=b\,</math>. With the help of <math>\,b</math> express
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
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	</div>{{#NAVCONTENT:Svar\|Svar 4.3:4\|Lösning a \|Lösning 4.3:4a\|Lösning b \|Lösning 4.3:4b\|Lösning c \|Lösning 4.3:4c\|Lösning d \|Lösning 4.3:4d\|Lösning e \|Lösning 4.3:4e\|Lösning f \|Lösning 4.3:4f}}		</div>{{#NAVCONTENT:Svar\|Svar 4.3:4\|Lösning a \|Lösning 4.3:4a\|Lösning b \|Lösning 4.3:4b\|Lösning c \|Lösning 4.3:4c\|Lösning d \|Lösning 4.3:4d\|Lösning e \|Lösning 4.3:4e\|Lösning f \|Lösning 4.3:4f}}

-	===~~Övning~~ 4.3:5===	+	===Exercise 4.3:5===
	<div class="ovning">		<div class="ovning">
-	~~För en spetsig vinkel~~ <math>\,v\,</math> ~~i en triangel gäller att~~ <math>\,\~~sin~~{v~~}=\displaystyle \frac{5}{7~~}\,</math>~~. Bestäm~~ <math>\,~~\cos{~~v}\,</math> ~~och~~ <math>\,\~~tan~~{v}\,</math>.	+	Determine <math>\,\cos{v}\,</math> and <math>\,\tan{v}\,</math>, where <math>\,v\,</math> is an acute angle in a triangle such that <math>\,\sin{v}=\displaystyle \frac{5}{7}\,</math>.
	</div>{{#NAVCONTENT:Svar\|Svar 4.3:5\|Lösning \|Lösning 4.3:5}}		</div>{{#NAVCONTENT:Svar\|Svar 4.3:5\|Lösning \|Lösning 4.3:5}}

-	===~~Övning~~ 4.3:6===	+	===Exercise 4.3:6===
	<div class="ovning">		<div class="ovning">
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
-	\|width="100%" \| ~~Bestäm~~ <math>\ \sin{v}\ </math> ~~och~~ <math>\ \tan{v}\ </math> om <math>\ \cos{v}=\displaystyle \frac{3}{4}\ </math> ~~och~~ <math>\ \displaystyle \frac{3\pi}{2} \leq v \leq 2\pi\,</math>.	+	\|width="100%" \| Determine <math>\ \sin{v}\ </math> and <math>\ \tan{v}\ </math> if <math>\ \cos{v}=\displaystyle \frac{3}{4}\ </math> and <math>\ \displaystyle \frac{3\pi}{2} \leq v \leq 2\pi\,</math>.
	\|-		\|-
	\|b)		\|b)
-	\|width="100%" \| ~~Bestäm~~ <math>\ \cos{v}\ </math> ~~och~~ <math>\ \tan{v}\ </math> om <math>\ \sin{v}=\displaystyle \frac{3}{10}\ </math> ~~och~~ <math>\,v\,</math> ~~ligger i den andra kvadranten~~.	+	\|width="100%" \| Determine <math>\ \cos{v}\ </math> and <math>\ \tan{v}\ </math> if <math>\ \sin{v}=\displaystyle \frac{3}{10}\ </math> and <math>\,v\,</math> lies in the second quadrant.
	\|-		\|-
	\|c)		\|c)
-	\|width="100%" \| ~~Bestäm~~ <math>\ \sin{v}\ </math> ~~och~~ <math>\ \cos{v}\ </math> om <math>\ \tan{v}=3\ </math> ~~och~~ <math>\ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,</math>.	+	\|width="100%" \| Determine <math>\ \sin{v}\ </math> and <math>\ \cos{v}\ </math> if <math>\ \tan{v}=3\ </math> and <math>\ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,</math>.
	\|}		\|}
	</div>{{#NAVCONTENT:Svar\|Svar 4.3:6\|Lösning a \|Lösning 4.3:6a\|Lösning b \|Lösning 4.3:6b\|Lösning c \|Lösning 4.3:6c}}		</div>{{#NAVCONTENT:Svar\|Svar 4.3:6\|Lösning a \|Lösning 4.3:6a\|Lösning b \|Lösning 4.3:6b\|Lösning c \|Lösning 4.3:6c}}

-	===~~Övning~~ 4.3:7===	+	===Exercise 4.3:7===
	<div class="ovning">		<div class="ovning">
-	~~Bestäm~~ <math>\ \sin{(x+y)}\ </math> om	+	Determine <math>\ \sin{(x+y)}\ </math> if
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
-	\|width="100%" \| <math>\sin{x}=\displaystyle \frac{2}{3}\,</math>,<math>\ \sin{y}=\displaystyle \frac{1}{3}\ </math> ~~och~~ <math>\,x\,</math>, <math> \,y\,</math> ~~är vinklar i första kvadranten~~.	+	\|width="100%" \| <math>\sin{x}=\displaystyle \frac{2}{3}\,</math>,<math>\ \sin{y}=\displaystyle \frac{1}{3}\ </math> and <math>\,x\,</math>, <math> \,y\,</math> are angles in the first quadrant.
	\|-		\|-
	\|b)		\|b)
-	\|width="100%" \| <math>\cos{x}=\displaystyle \frac{2}{5}\,</math>, <math>\ \cos{y}=\displaystyle \frac{3}{5}\ </math> ~~och~~ <math>\,x\,</math>, <math>\,y\,</math> ~~är vinklar i första kvadranten~~.	+	\|width="100%" \| <math>\cos{x}=\displaystyle \frac{2}{5}\,</math>, <math>\ \cos{y}=\displaystyle \frac{3}{5}\ </math> and <math>\,x\,</math>, <math>\,y\,</math> are angles in the first quadrant.
	\|}		\|}
	</div>{{#NAVCONTENT:Svar\|Svar 4.3:7\|Lösning a \|Lösning 4.3:7a\|Lösning b \|Lösning 4.3:7b}}		</div>{{#NAVCONTENT:Svar\|Svar 4.3:7\|Lösning a \|Lösning 4.3:7a\|Lösning b \|Lösning 4.3:7b}}

-	===~~Övning~~ 4.3:8===	+	===Exercise 4.3:8===
	<div class="ovning">		<div class="ovning">
-	~~Visa följande trigonometriska samband~~	+	Show the following trigonometric relations
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
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	</div>{{#NAVCONTENT:Lösning a \|Lösning 4.3:8a\|Lösning b \|Lösning 4.3:8b\|Lösning c \|Lösning 4.3:8c\|Lösning d \|Lösning 4.3:8d}}		</div>{{#NAVCONTENT:Lösning a \|Lösning 4.3:8a\|Lösning b \|Lösning 4.3:8b\|Lösning c \|Lösning 4.3:8c\|Lösning d \|Lösning 4.3:8d}}

-	===~~Övning~~ 4.3:9===	+	===Exercise 4.3:9===
	<div class="ovning">		<div class="ovning">
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|		\|
-	\|width="100%" \| ~~Visa "Morries formel"~~	+	\|width="100%" \| Show Feynman's equality
	\|-		\|-
	\|		\|
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	\|-		\|-
	\|		\|
-	\|width="100%" \|(~~Ledtråd~~: ~~Använd formeln för dubbla vinkeln på~~ <math>\,\sin 160^\circ\,</math>.)	+	\|width="100%" \|(Hint: use the formula for double angles on <math>\,\sin 160^\circ\,</math>.)
	\|}		\|}
	</div>{{#NAVCONTENT:Lösning \|Lösning 4.3:9}}		</div>{{#NAVCONTENT:Lösning \|Lösning 4.3:9}}

Tek: Regenerate images and tabs

2008-06-13T16:59:54Z

Regenerate images and tabs

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	{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"		{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
-	{{~~Mall:~~Ej vald flik\|[[4.3 Trigonometriska samband\|Teori]]}}	+	{{Ej vald flik\|[[4.3 Trigonometriska samband\|Teori]]}}
-	{{~~Mall:~~Vald flik\|[[4.3 Övningar\|Övningar]]}}	+	{{Vald flik\|[[4.3 Övningar\|Övningar]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|
	\|}		\|}

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	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
	{{Not selected tab\|[[4.3 Trigonometric relations\|Theory]]}}		{{Not selected tab\|[[4.3 Trigonometric relations\|Theory]]}}
-	{{~~Vald flik~~\|[[4.3 Exercises\|Exercises]]}}	+	{{Selected tab\|[[4.3 Exercises\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|
	\|}		\|}

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	{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"		{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
-	{{~~Ej vald flik~~\|[[4.3 Trigonometric relations\|Theory]]}}	+	{{Not selected tab\|[[4.3 Trigonometric relations\|Theory]]}}
	{{Vald flik\|[[4.3 Exercises\|Exercises]]}}		{{Vald flik\|[[4.3 Exercises\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|

←Older revision		Revision as of 13:38, 10 September 2008
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	{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"		{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
-	{{Ej vald flik\|[[4.3 ~~Trigonometriska samband~~\|Theory]]}}	+	{{Ej vald flik\|[[4.3 Trigonometric relations\|Theory]]}}
	{{Vald flik\|[[4.3 Exercises\|Exercises]]}}		{{Vald flik\|[[4.3 Exercises\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|

←Older revision		Revision as of 10:49, 10 September 2008
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	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
	{{Ej vald flik\|[[4.3 Trigonometriska samband\|Theory]]}}		{{Ej vald flik\|[[4.3 Trigonometriska samband\|Theory]]}}
-	{{Vald flik\|[[4.3 ~~Övningar~~\|Exercises]]}}	+	{{Vald flik\|[[4.3 Exercises\|Exercises]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|
	\|}		\|}

←Older revision		Revision as of 16:59, 13 June 2008
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	{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"		{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
	\| style="border-bottom:1px solid #000" width="5px" \|		\| style="border-bottom:1px solid #000" width="5px" \|
-	{{~~Mall:~~Ej vald flik\|[[4.3 Trigonometriska samband\|Teori]]}}	+	{{Ej vald flik\|[[4.3 Trigonometriska samband\|Teori]]}}
-	{{~~Mall:~~Vald flik\|[[4.3 Övningar\|Övningar]]}}	+	{{Vald flik\|[[4.3 Övningar\|Övningar]]}}
	\| style="border-bottom:1px solid #000" width="100%"\|		\| style="border-bottom:1px solid #000" width="100%"\|
	\|}		\|}