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4.1 Exercises

From Förberedande kurs i matematik 1

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       Theory          Exercises      

Exercise 4.1:1

Write in degrees and radians

a) 41 revolution b) 83 revolution
c) −32 revolution d) 1297 revolution

Answer | Solution

Exrecise 4.1:2

Transform to radians

a) 45 b) 135 c) −63 d) 270

Answer | Solution

Exercise 4.1:3

Determine the length of the side marked x.

a)

[Image]

b)

[Image]

c)

[Image]

Answer | Solution a | Solution b | Solution c

Exercise 4.1:4

a) Determine the distance between the points (1,1) and (5,4).
b) Determine the distance between the points(-2,5) and (3,-1).
c) Find the point on the x-axis which lies as far from the point (3,3) as from (5,1).

Answer | Solution a | Solution b | Solution c

Exercise 4.1:5

a) Determine the equation of a circle having its centre at (1,2) and radius 2.
b) Determine the equation of a circle having its centre at (2,-1) and which contains the point (-1,1).

Answer | Solution a | Solution b

Exercise 4.1:6

Sketch the following circles

a) x2+y2=9 b) (x−1)2+(y−2)2=3
c) (3x−1)2+(3y+7)2=10

Answer | Solution a | Solution b | Solution c

Exercise 4.1:7

Sketch the following circles

a) x2+2x+y2−2y=1 b) x2+y2+4y=0
c) x2−2x+y2+6y=−3 d) x2−2x+y2+2y=−2

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

Exercise 4.1:8

How many revolutions does a wheel of radius 50 cm make when it rolls 10m?

Answer | Solution

Exercise 4.1:9

On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds?

Answer | Solution


Exercise 4.1:10

A washing line of length 5.4 m hangs between two vertical trees that are at a distance of 4.8 m from each other. One end of the line is fixed 0.6 m higher than the other, and a jacket hangs from a hanger 1.2 m from the tree where the line has its lower point of attachment. Determine how far below the lower attachement point the hanger is hanging. (That is, the distance \displaystyle \,x\, in the figure).


[Image]

Answer | Solution

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