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4.2 Exercises

From Förberedande kurs i matematik 1

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Revision as of 07:27, 16 September 2008

       Theory          Exercises      

Exercise 4.2:1

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

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)

[Image]

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 | 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 - Figur - Rätvinklig triangel med vinkeln v och sidor 2 och 5 b)

[Image]

c)

[Image]

d) 4.2 - Figur - Rätvinklig triangel med vinkeln v och sidor 3 och 5
e)

[Image]

f)

[Image]

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.

[Image]

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?

[Image]

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.

[Image]

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.)

[Image]

Answer | Solution

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