4.2 Exercises
From Förberedande kurs i matematik 1
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{{:4.2 - Figur - Rätvinklig triangel med vinkeln 50° och sidor x och 19}} | {{:4.2 - Figur - Rätvinklig triangel med vinkeln 50° och sidor x och 19}} | ||
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| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:1|Solution a |Lösning 4.2:1a|Solution b |Lösning 4.2:1b|Solution c |Lösning 4.2:1c|Solution d |Lösning 4.2:1d|Solution e |Lösning 4.2:1e|Solution f |Lösning 4.2:1f}} |
===Exercise 4.2:2=== | ===Exercise 4.2:2=== | ||
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|width="50%" | {{:4.2 - Figur - Likbent triangel med toppvinkeln v och sidor 2, 3 och 3}} | |width="50%" | {{:4.2 - Figur - Likbent triangel med toppvinkeln v och sidor 2, 3 och 3}} | ||
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| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:2|Solution a |Lösning 4.2:2a|Solution b |Lösning 4.2:2b|Solution c |Lösning 4.2:2c|Solution d |Lösning 4.2:2d|Solution e |Lösning 4.2:2e|Solution f |Lösning 4.2:2f}} |
===Exercise 4.2:3=== | ===Exercise 4.2:3=== | ||
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|width="33%" | <math>\cos{\left(-\displaystyle \frac{\pi}{6}\right)}</math> | |width="33%" | <math>\cos{\left(-\displaystyle \frac{\pi}{6}\right)}</math> | ||
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| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:3|Solution a |Lösning 4.2:3a|Solution b |Lösning 4.2:3b|Solution c |Lösning 4.2:3c|Solution d |Lösning 4.2:3d|Solution e |Lösning 4.2:3e|Solution f |Lösning 4.2:3f}} |
===Exercise 4.2:4=== | ===Exercise 4.2:4=== | ||
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|width="33%" | <math>\tan{\left(-\displaystyle \frac{5\pi}{3}\right)}</math> | |width="33%" | <math>\tan{\left(-\displaystyle \frac{5\pi}{3}\right)}</math> | ||
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| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:4|Solution a |Lösning 4.2:4a|Solution b |Lösning 4.2:4b|Solution c |Lösning 4.2:4c|Solution d |Lösning 4.2:4d|Solution e |Lösning 4.2:4e|Solution f |Lösning 4.2:4f}} |
===Exercise 4.2:5=== | ===Exercise 4.2:5=== | ||
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|width="25%" | <math>\tan{495^\circ}</math> | |width="25%" | <math>\tan{495^\circ}</math> | ||
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| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:5|Solution a |Lösning 4.2:5a|Solution b |Lösning 4.2:5b|Solution c |Lösning 4.2:5c|Solution d |Lösning 4.2:5d}} |
===Exercise 4.2:6=== | ===Exercise 4.2:6=== | ||
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|width="100%" | <center> {{:4.2 - Figur - Två trianglar med vinklar 45° resp. 60° och höjdskillnad x}} </center> | |width="100%" | <center> {{:4.2 - Figur - Två trianglar med vinklar 45° resp. 60° och höjdskillnad x}} </center> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:6|Solution |Lösning 4.2:6}} |
===Exercise 4.2:7=== | ===Exercise 4.2:7=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | In order to determine the width of a river, we measure from two points, A and B on one side of the straight bank to a tree, C on the opposite side. How wide is the river if the measurements in the figure are correct? | + | In order to determine the width of a river, we measure from two points, A and B on one side of the straight bank to a tree, C, on the opposite side. How wide is the river if the measurements in the figure are correct? |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
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|width="100%" | <center> {{:4.2 - Figur - Älv}} </center> | |width="100%" | <center> {{:4.2 - Figur - Älv}} </center> | ||
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| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:7|Solution |Lösning 4.2:7}} |
===Exercise 4.2:8=== | ===Exercise 4.2:8=== | ||
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|width="100%" | <center> {{:4.2 - Figur - Hängande stång}} </center> | |width="100%" | <center> {{:4.2 - Figur - Hängande stång}} </center> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:8|Solution |Lösning 4.2:8}} |
===Exercise 4.2:9=== | ===Exercise 4.2:9=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | The road from ''A'' to ''B'' consists of three straight parts ''AP'', ''PQ'' and ''QB'', which are 4 | + | The road from ''A'' to ''B'' consists of three straight parts ''AP'', ''PQ'' and ''QB'', which are 4.0 km, 12.0 km and 5.0 km respectively. The angles marked at ''P'' and ''Q'' in the figure are 30° and 90° respectively. Calculate the distance as the crow flies from ''A'' to ''B''. (The exercise is taken from the Swedish National Exam in Mathematics, November 1976, although slightly modified.) |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
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|width="100%" | <center> {{:4.2 - Figur - Bilväg från A till B via P och Q}} </center> | |width="100%" | <center> {{:4.2 - Figur - Bilväg från A till B via P och Q}} </center> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.2:9|Solution |Lösning 4.2:9}} |
Revision as of 14:19, 19 August 2008
| Theory | Exercises |
Exercise 4.2:1
Using the trigonometric functions, determine the length of the side marked\displaystyle \,x\,
Answer
Loading...
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 4.2:2
Determine a trigonometric equation that is satisfied by \displaystyle \,v\,.
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 4.2:3
Determine
| a) | \displaystyle \sin{\left(-\displaystyle \frac{\pi}{2}\right)} | b) | \displaystyle \cos{2\pi} | c) | \displaystyle \sin{9\pi} |
| d) | \displaystyle \cos{\displaystyle \frac{7\pi}{2}} | e) | \displaystyle \sin{\displaystyle \frac{3\pi}{4}} | f) | \displaystyle \cos{\left(-\displaystyle \frac{\pi}{6}\right)} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 4.2:4
Determine
| a) | \displaystyle \cos{\displaystyle \frac{11\pi}{6}} | b) | \displaystyle \cos{\displaystyle \frac{11\pi}{3}} | c) | \displaystyle \tan{\displaystyle \frac{3\pi}{4}} |
| d) | \displaystyle \tan{\pi} | e) | \displaystyle \tan{\displaystyle \frac{7\pi}{6}} | f) | \displaystyle \tan{\left(-\displaystyle \frac{5\pi}{3}\right)} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 4.2:5
Determine
| a) | \displaystyle \cos{135^\circ} | b) | \displaystyle \tan{225^\circ} | c) | \displaystyle \cos{330^\circ} | d) | \displaystyle \tan{495^\circ} |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 4.2:6
Determine the length of the side marked \displaystyle \,x\,.
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Answer
Solution
Exercise 4.2:7
In order to determine the width of a river, we measure from two points, A and B on one side of the straight bank to a tree, C, on the opposite side. How wide is the river if the measurements in the figure are correct?
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Answer
Solution
Exercise 4.2:8
A rod of length \displaystyle \,\ell\, hangs from two ropes of length \displaystyle \,a\, and \displaystyle \,b\, as shown in the figure. The ropes make angles \displaystyle \,\alpha\, and \displaystyle \,\beta\, with the vertical. Determine a trigonometric equation for the angle \displaystyle \,\gamma\, which the rod makes with the vertical.
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Answer
Solution
Exercise 4.2:9
The road from A to B consists of three straight parts AP, PQ and QB, which are 4.0 km, 12.0 km and 5.0 km respectively. The angles marked at P and Q in the figure are 30° and 90° respectively. Calculate the distance as the crow flies from A to B. (The exercise is taken from the Swedish National Exam in Mathematics, November 1976, although slightly modified.)
| |
Answer
Solution
