4.1 Exercises

From Förberedande kurs i matematik 1

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{{Not selected tab|[[4.1 Angles and circles|Theory]]}}
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{{Selected tab|[[4.1 Exercises|Exercises]]}}
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{{:4.1 - Figur - Rätvinklig triangel med sidor 12, x och 13}}
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===Exercise 4.1:1===
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<div class="ovning">
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Write in degrees and radians
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{| width="100%" cellspacing="10px"
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|a)
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|width="50%" | <math>\displaystyle \frac{1}{4} \textrm{ revolution} </math>
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|b)
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|width="50%" | <math>\displaystyle \frac{3}{8} \textrm{ revolution}</math>
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|-
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|c)
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|width="50%" | <math>-\displaystyle \frac{2}{3}\textrm{ revolution}</math>
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|d)
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|width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ revolution} </math>
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|}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:1|Solution |Solution 4.1:1}}
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{{:4.1 - Figur - Rätvinklig triangel med sidor 8, x och 17}}
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===Exrecise 4.1:2===
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<div class="ovning">
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Transform to radians
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{| width="100%" cellspacing="10px"
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|a)
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|width="25%" | <math>45^\circ</math>
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|b)
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|width="25%" | <math>135^\circ</math>
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|c)
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|width="25%" | <math>-63^\circ</math>
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|d)
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|width="25%" | <math>270^\circ</math>
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|}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:2|Solution |Solution 4.1:2}}
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{{:4.1 - Figur - Tvättlina med kavaj på galge}}
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===Exercise 4.1:3===
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<div class="ovning">
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Determine the length of the side marked <math>\,x\,\mbox{.}</math>
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{| width="100%" cellspacing="10px"
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|a)
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|width="33%" |
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{{:4.1 - Figure - A right-angled triangle with sides 30, 40 and x}}
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|b)
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|width="33%" | {{:4.1 - Figure - A right-angled triangle with sides 12, x and 13}}
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|c)
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|width="33%" | {{:4.1 - Figure - A right-angled triangle with sides 8, x and 17}}
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|}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:3|Solution a|Solution 4.1:3a|Solution b|Solution 4.1:3b|Solution c|Solution 4.1:3c}}
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===Exercise 4.1:4===
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<div class="ovning">
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{| width="100%" cellspacing="10px"
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|a)
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|width="100%" | Determine the distance between the points (1,1) and (5,4).
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|-
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|b)
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|width="100%" | Determine the distance between the points(-2,5) and (3,-1).
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|-
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|c)
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|width="100%" | Find the point on the x-axis which lies as far from the point (3,3) as from (5,1).
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|}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:4|Solution a|Solution 4.1:4a|Solution b|Solution 4.1:4b|Solution c|Solution 4.1:4c}}
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===Exercise 4.1:5===
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<div class="ovning">
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{| width="100%" cellspacing="10px"
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|a)
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|width="100%" | Determine the equation of a circle having its centre at (1,2) and radius 2.
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|-
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|b)
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|width="100%" | Determine the equation of a circle having its centre at (2,-1) and which contains the point (-1,1).
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|}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:5|Solution a|Solution 4.1:5a|Solution b|Solution 4.1:5b}}
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===Exercise 4.1:6===
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<div class="ovning">
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Sketch the following circles
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{| width="100%" cellspacing="10px"
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|a)
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|width="50%" | <math>x^2+y^2=9</math>
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|b)
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|width="50%" | <math>(x-1)^2+(y-2)^2=3</math>
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|-
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|c)
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|width="50%" | <math>(3x-1)^2+(3y+7)^2=10</math>
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|}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:6|Solution a|Solution 4.1:6a|Solution b|Solution 4.1:6b|Solution c|Solution 4.1:6c}}
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===Exercise 4.1:7===
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<div class="ovning">
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Sketch the following circles
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{| width="100%" cellspacing="10px"
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|a)
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|width="50%" | <math>x^2+2x+y^2-2y=1</math>
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|b)
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|width="50%" | <math>x^2+y^2+4y=0</math>
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|-
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|c)
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|width="50%" | <math>x^2-2x+y^2+6y=-3</math>
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|d)
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|width="50%" | <math>x^2-2x+y^2+2y=-2</math>
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|}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:7|Solution a|Solution 4.1:7a|Solution b|Solution 4.1:7b|Solution c|Solution 4.1:7c|Solution d|Solution 4.1:7d}}
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===Exercise 4.1:8===
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<div class="ovning">
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How many revolutions does a wheel of radius 50 cm make when it rolls 10m?
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</div>{{#NAVCONTENT:Answer|Answer 4.1:8|Solution|Solution 4.1:8}}
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===Exercise 4.1:9===
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<div class="ovning">
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On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds?
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</div>{{#NAVCONTENT:Answer|Answer 4.1:9|Solution|Solution 4.1:9}}
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===Exercise 4.1:10===
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<div class="ovning">
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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
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hanger 1.2 m from the tree where the line has its lower point of attachment. Determine how far below the
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lower attachement point the hanger is hanging. (That is, the distance <math>\,x\,</math> in the figure).
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<center> {{:4.1 - Figure - A washing line with a jacket on a hanger}} </center>
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</div>{{#NAVCONTENT:Answer|Answer 4.1:10|Solution|Solution 4.1:10}}

Current revision

       Theory          Exercises      

Exercise 4.1:1

Write in degrees and radians

a) \displaystyle \displaystyle \frac{1}{4} \textrm{ revolution} b) \displaystyle \displaystyle \frac{3}{8} \textrm{ revolution}
c) \displaystyle -\displaystyle \frac{2}{3}\textrm{ revolution} d) \displaystyle \displaystyle \frac{97}{12} \textrm{ revolution}
Answer
Answer 4.1:1
Solution
Solution 4.1:1

Exrecise 4.1:2

Transform to radians

a) \displaystyle 45^\circ b) \displaystyle 135^\circ c) \displaystyle -63^\circ d) \displaystyle 270^\circ
Answer
Answer 4.1:2
Solution
Solution 4.1:2

Exercise 4.1:3

Determine the length of the side marked \displaystyle \,x\,\mbox{.}

a)

[Image]

b)

[Image]

c)

[Image]

Answer
Answer 4.1:3
Solution a
Solution 4.1:3a
Solution b
Solution 4.1:3b
Solution c
Solution 4.1:3c

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
Answer 4.1:4
Solution a
Solution 4.1:4a
Solution b
Solution 4.1:4b
Solution c
Solution 4.1:4c

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
Answer 4.1:5
Solution a
Solution 4.1:5a
Solution b
Solution 4.1:5b

Exercise 4.1:6

Sketch the following circles

a) \displaystyle x^2+y^2=9 b) \displaystyle (x-1)^2+(y-2)^2=3
c) \displaystyle (3x-1)^2+(3y+7)^2=10
Answer
Answer 4.1:6
Solution a
Solution 4.1:6a
Solution b
Solution 4.1:6b
Solution c
Solution 4.1:6c

Exercise 4.1:7

Sketch the following circles

a) \displaystyle x^2+2x+y^2-2y=1 b) \displaystyle x^2+y^2+4y=0
c) \displaystyle x^2-2x+y^2+6y=-3 d) \displaystyle x^2-2x+y^2+2y=-2
Answer
Answer 4.1:7
Solution a
Solution 4.1:7a
Solution b
Solution 4.1:7b
Solution c
Solution 4.1:7c
Solution d
Solution 4.1:7d

Exercise 4.1:8

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

Answer
Answer 4.1:8
Solution
Solution 4.1:8

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
Answer 4.1:9
Solution
Solution 4.1:9


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
Answer 4.1:10
Solution
Solution 4.1:10
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