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:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 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:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 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:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 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:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:6|Solution |Lösning 4.2:6}} |
===Exercise 4.2:7=== | ===Exercise 4.2:7=== | ||
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|width="100%" | <center> {{:4.2 - Figur - Älv}} </center> | |width="100%" | <center> {{:4.2 - Figur - Älv}} </center> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 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:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:8|Solution |Lösning 4.2:8}} |
===Exercise 4.2:9=== | ===Exercise 4.2:9=== | ||
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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:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:9|Solution |Lösning 4.2:9}} |
Revision as of 07:11, 9 September 2008
| Theory | Exercises |
Exercise 4.2:1
Using the trigonometric functions, determine the length of the side marked
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Loading...Exercise 4.2:2
Determine a trigonometric equation that is satisfied by
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 4.2:3
Determine
| a) |  − 2 | b) | | c) | |
| d) | | e) | | f) | −6 |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 4.2:4
Determine
| a) | | b) | | c) | |
| d) | | e) | | f) |  −35 |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 4.2:5
Determine
| a) |  | b) | | c) | | d) | |
Answer | Solution a | Solution b | Solution c | Solution d
Exercise 4.2:6
Determine the length of the side marked
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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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Exercise 4.2:8
A rod of length 
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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.)
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