4.2 Exercises

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Revision as of 10:48, 10 September 2008

       Theory          Exercises      

Exercise 4.2:1

Using the trigonometric functions, determine the length of the side marked\displaystyle \,x\,

a) 4.2 - Figur - Rätvinklig triangel med vinkeln 27° och sidor x och 13 b)

4.2 - Figur - Rätvinklig triangel med vinkeln 32° och sidor x och 25

c) 4.2 - Figur - Rätvinklig triangel med vinkeln 40° och sidor 14 och x d) 4.2 - Figur - Rätvinklig triangel med vinkeln 20° och sidor 16 och x
e) 4.2 - Figur - Rätvinklig triangel med vinkeln 35° och sidor 11 och x f)

4.2 - Figur - Rätvinklig triangel med vinkeln 50° och sidor x och 19

Answer
Answer 4.2:1
Solution a
Solution 4.2:1a
Solution b
Solution 4.2:1b
Solution c
Solution 4.2:1c
Solution d
Solution 4.2:1d
Solution e
Solution 4.2:1e
Solution f
Solution 4.2:1f

Exercise 4.2:2

Determine a trigonometric equation that is satisfied by \displaystyle \,v\,.

a) 4.2 - Figur - Rätvinklig triangel med vinkeln v och sidor 2 och 5 b) 4.2 - Figur - Rätvinklig triangel med vinkeln v och sidor 70 och 110
c) 4.2 - Figur - Rätvinklig triangel med vinkeln v och sidor 5 och 7 d) 4.2 - Figur - Rätvinklig triangel med vinkeln v och sidor 3 och 5
e) 4.2 - Figur - Rätvinklig triangel med vinklar v och 60° och sidan 5 f) 4.2 - Figur - Likbent triangel med toppvinkeln v och sidor 2, 3 och 3
Answer
Answer 4.2:2
Solution a
Solution 4.2:2a
Solution b
Solution 4.2:2b
Solution c
Solution 4.2:2c
Solution d
Solution 4.2:2d
Solution e
Solution 4.2:2e
Solution f
Solution 4.2:2f

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
Answer 4.2:3
Solution a
Solution 4.2:3a
Solution b
Solution 4.2:3b
Solution c
Solution 4.2:3c
Solution d
Solution 4.2:3d
Solution e
Solution 4.2:3e
Solution f
Solution 4.2:3f

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
Answer 4.2:4
Solution a
Solution 4.2:4a
Solution b
Solution 4.2:4b
Solution c
Solution 4.2:4c
Solution d
Solution 4.2:4d
Solution e
Solution 4.2:4e
Solution f
Solution 4.2:4f

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
Answer 4.2:5
Solution a
Solution 4.2:5a
Solution b
Solution 4.2:5b
Solution c
Solution 4.2:5c
Solution d
Solution 4.2:5d

Exercise 4.2:6

Determine the length of the side marked \displaystyle \,x\,.

4.2 - Figur - Två trianglar med vinklar 45° resp. 60° och höjdskillnad x
Answer
Answer 4.2:6
Solution
Solution 4.2:6

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?

4.2 - Figur - Älv
Answer
Answer 4.2:7
Solution
Solution 4.2:7

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.

4.2 - Figur - Hängande stång
Answer
Answer 4.2:8
Solution
Solution 4.2:8

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.)

4.2 - Figur - Bilväg från A till B via P och Q
Answer
Answer 4.2:9
Solution
Solution 4.2:9
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