4.1 Övningar

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{{Mall:Ej vald flik|[[4.1 Vinklar och cirklar|Teori]]}}
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{{Ej vald flik|[[4.1 Vinklar och cirklar|Theory]]}}
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{{Mall:Vald flik|[[4.1 Övningar|Övningar]]}}
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{{Vald flik|[[4.1 Övningar|Exercises]]}}
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===Övning 4.1:1===
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===Exercise 4.1:1===
<div class="ovning">
<div class="ovning">
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Skriv i grader och radianer
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Write in degrees and radians
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="50%" | <math>\displaystyle \frac{1}{4} \textrm{ varv} $</math>
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|width="50%" | <math>\displaystyle \frac{1}{4} \textrm{ revolution} </math>
|b)
|b)
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|width="50%" | <math>\displaystyle \frac{3}{8} \textrm{ varv}</math>
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|width="50%" | <math>\displaystyle \frac{3}{8} \textrm{ revolution}</math>
|-
|-
|c)
|c)
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|width="50%" | <math>-\displaystyle \frac{2}{3}\textrm{ varv}</math>
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|width="50%" | <math>-\displaystyle \frac{2}{3}\textrm{ revolution}</math>
|d)
|d)
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|width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ varv} </math>
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|width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ revolution} </math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:1|Lösning a|Lösning 4.1:1a|Lösning b|Lösning 4.1:1b|Lösning c|Lösning 4.1:1c|Lösning d|Lösning 4.1:1d}}
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</div>{{#NAVCONTENT:Answer|Svar 4.1:1|Solution |Lösning 4.1:1}}
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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|Svar 4.1:2|Solution |Lösning 4.1:2}}
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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%" |
{{:4.1 - Figur - Rätvinklig triangel med sidor 30, 40 och x}}
{{:4.1 - Figur - Rätvinklig triangel med sidor 30, 40 och x}}
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|b)
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|width="33%" | {{:4.1 - Figur - Rätvinklig triangel med sidor 12, x och 13}}
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|c)
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|width="33%" | {{:4.1 - Figur - Rätvinklig triangel med sidor 8, x och 17}}
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|}
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</div>{{#NAVCONTENT:Answer|Svar 4.1:3|Solution a|Lösning 4.1:3a|Solution b|Lösning 4.1:3b|Solution c|Lösning 4.1:3c}}
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{{:4.1 - Figur - Rätvinklig triangel med sidor 12, x och 13}}
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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|Svar 4.1:4|Solution a|Lösning 4.1:4a|Solution b|Lösning 4.1:4b|Solution c|Lösning 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|Svar 4.1:5|Solution a|Lösning 4.1:5a|Solution b|Lösning 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)
 +
|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|Svar 4.1:6|Solution a|Lösning 4.1:6a|Solution b|Lösning 4.1:6b|Solution c|Lösning 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"
 +
|a)
 +
|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|Svar 4.1:7|Solution a|Lösning 4.1:7a|Solution b|Lösning 4.1:7b|Solution c|Lösning 4.1:7c|Solution d|Lösning 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|Svar 4.1:8|Solution|Lösning 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|Svar 4.1:9|Solution|Lösning 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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{{:4.1 - Figur - Rätvinklig triangel med sidor 8, x och 17}}
 
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{{:4.1 - Figur - Tvättlina med kavaj på galge}}
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<center> {{:4.1 - Figur - Tvättlina med kavaj på galge}} </center>
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</div>{{#NAVCONTENT:Answer|Svar 4.1:10|Solution|Lösning 4.1:10}}

Aktuelle Version

       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
Svar 4.1:1
Solution
Lösning 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
Svar 4.1:2
Solution
Lösning 4.1:2

Exercise 4.1:3

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

a)

[Image]

b)

[Image]

c)

[Image]

Answer
Svar 4.1:3
Solution a
Lösning 4.1:3a
Solution b
Lösning 4.1:3b
Solution c
Lösning 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
Svar 4.1:4
Solution a
Lösning 4.1:4a
Solution b
Lösning 4.1:4b
Solution c
Lösning 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
Svar 4.1:5
Solution a
Lösning 4.1:5a
Solution b
Lösning 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
Svar 4.1:6
Solution a
Lösning 4.1:6a
Solution b
Lösning 4.1:6b
Solution c
Lösning 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
Svar 4.1:7
Solution a
Lösning 4.1:7a
Solution b
Lösning 4.1:7b
Solution c
Lösning 4.1:7c
Solution d
Lösning 4.1:7d

Exercise 4.1:8

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

Answer
Svar 4.1:8
Solution
Lösning 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
Svar 4.1:9
Solution
Lösning 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
Svar 4.1:10
Solution
Lösning 4.1:10
Von „http://wiki.sommarmatte.se/wikis/2008/bridgecourse1-TU-Berlin/index.php/4.1_%C3%96vningar“