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4.2 Übungen

Aus Online Mathematik Brückenkurs 1

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Version vom 10:09, 21. Okt. 2008

 

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Exercise 4.2:1

Using the trigonometric functions, determine the length of the side markedx

a)

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b)

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c)

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d)

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e)

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f)

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Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.2:2

Determine a trigonometric equation that is satisfied by v.

a) 4.2 - Figure - A right-angled triangle with angle v and sides 2 and 5 b) 4.2 - Figure - A right-angled triangle with angle v and sides 70 and 110
c) 4.2 - Figure - A right-angled triangle with angle v and sides 5 and 7 d) 4.2 - Figure - A right-angled triangle with angle v and sides 3 and 5
e) 4.2 - Figure - A right-angled triangle with angles v and 60° and side 5 f) 4.2 - Figure - An isosceles triangle with top angle v and sides 2, 3 and 3

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.2:3

Determine

a) sin−2  b) cos2 c) sin9
d) cos27 e) sin43 f) cos−6 

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.2:4

Determine

a) cos611 b) cos311 c) tan43
d) tan e) tan67 f) tan−35 

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.2:5

Determine

a) cos135 b) tan225 c) cos330 d) tan495

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 4.2:6

Determine the length of the side marked x.

4.2 - Figure - Two triangles with angles 45° and 60°, respectively, and height difference x

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?

4.2 - Figure - A river

Answer | Solution

Exercise 4.2:8

A rod of length hangs from two ropes of length a and b as shown in the figure. The ropes make angles and with the vertical. Determine a trigonometric equation for the angle which the rod makes with the vertical.

4.2 - Figure - Hanging rod

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.)

4.2 - Figure - A road from A to B via P and Q

Answer | Solution

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