4.1 Exercises

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{{Ej vald flik|[[4.1 Vinklar och cirklar|Teori]]}}
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{{Not selected tab|[[4.1 Angles and circles|Theory]]}}
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{{Vald flik|[[4.1 Övningar|Övningar]]}}
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{{Selected tab|[[4.1 Exercises|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 |Lösning 4.1:1}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:1|Solution |Solution 4.1:1}}
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===Övning 4.1:2===
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===Exrecise 4.1:2===
<div class="ovning">
<div class="ovning">
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Omvandla till radianer
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Transform to radians
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="25%" | <math>270^\circ</math>
|width="25%" | <math>270^\circ</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:2|Lösning |Lösning 4.1:2}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:2|Solution |Solution 4.1:2}}
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===Övning 4.1:3===
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===Exercise 4.1:3===
<div class="ovning">
<div class="ovning">
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Bestäm längden av sidan som är markerad med <math>\,x\,\mbox{.}</math>
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Determine the length of the side marked <math>\,x\,\mbox{.}</math>
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
|width="33%" |
|width="33%" |
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{{:4.1 - Figur - Rätvinklig triangel med sidor 30, 40 och x}}
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{{:4.1 - Figure - A right-angled triangle with sides 30, 40 and x}}
|b)
|b)
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|width="33%" | {{:4.1 - Figur - Rätvinklig triangel med sidor 12, x och 13}}
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|width="33%" | {{:4.1 - Figure - A right-angled triangle with sides 12, x and 13}}
|c)
|c)
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|width="33%" | {{:4.1 - Figur - Rätvinklig triangel med sidor 8, x och 17}}
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|width="33%" | {{:4.1 - Figure - A right-angled triangle with sides 8, x and 17}}
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:3|Lösning a|Lösning 4.1:3a|Lösning b|Lösning 4.1:3b|Lösning c|Lösning 4.1:3c}}
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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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===Övning 4.1:4===
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===Exercise 4.1:4===
<div class="ovning">
<div class="ovning">
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="100%" | Bestäm avståndet mellan punkterna (1,1) och (5,4).
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|width="100%" | Determine the distance between the points (1,1) and (5,4).
|-
|-
|b)
|b)
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|width="100%" | Bestäm avståndet mellan punkterna (-2,5) och (3,-1).
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|width="100%" | Determine the distance between the points(-2,5) and (3,-1).
|-
|-
|c)
|c)
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|width="100%" | Hitta den punkt på x-axeln som ligger lika långt från punkterna (3,3) och (5,1).
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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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</div>{{#NAVCONTENT:Svar|Svar 4.1:4|Lösning a|Lösning 4.1:4a|Lösning b|Lösning 4.1:4b|Lösning c|Lösning 4.1:4c}}
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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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===Övning 4.1:5===
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===Exercise 4.1:5===
<div class="ovning">
<div class="ovning">
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="100%" | Bestäm ekvationen för en cirkel med medelpunkt i (1,2) och radie 2.
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|width="100%" | Determine the equation of a circle having its centre at (1,2) and radius 2.
|-
|-
|b)
|b)
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|width="100%" | Bestäm ekvationen för den cirkel som har medelpunkt i (2,-1) och innehåller punkten (-1,1).
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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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</div>{{#NAVCONTENT:Svar|Svar 4.1:5|Lösning a|Lösning 4.1:5a|Lösning b|Lösning 4.1:5b}}
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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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===Övning 4.1:6===
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===Exercise 4.1:6===
<div class="ovning">
<div class="ovning">
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Skissera följande cirklar
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Sketch the following circles
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 89: Line 89:
|width="50%" | <math>(3x-1)^2+(3y+7)^2=10</math>
|width="50%" | <math>(3x-1)^2+(3y+7)^2=10</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:6|Lösning a|Lösning 4.1:6a|Lösning b|Lösning 4.1:6b|Lösning c|Lösning 4.1:6c}}
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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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===Övning 4.1:7===
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===Exercise 4.1:7===
<div class="ovning">
<div class="ovning">
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Skissera följande cirklar
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Sketch the following circles
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 105: Line 105:
|width="50%" | <math>x^2-2x+y^2+2y=-2</math>
|width="50%" | <math>x^2-2x+y^2+2y=-2</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 4.1:7|Lösning a|Lösning 4.1:7a|Lösning b|Lösning 4.1:7b|Lösning c|Lösning 4.1:7c|Lösning d|Lösning 4.1:7d}}
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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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===Övning 4.1:8===
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===Exercise 4.1:8===
<div class="ovning">
<div class="ovning">
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Hur många varv snurrar ett hjul med radie 50 cm när det rullar 10m?
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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:Svar|Svar 4.1:8|Lösning|Lösning 4.1:8}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:8|Solution|Solution 4.1:8}}
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===Övning 4.1:9===
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===Exercise 4.1:9===
<div class="ovning">
<div class="ovning">
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På en klocka är sekundvisaren 8 cm lång. Hur stor area sveper den över på 10 sekunder?
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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:Svar|Svar 4.1:9|Lösning|Lösning 4.1:9}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:9|Solution|Solution 4.1:9}}
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===Övning 4.1:10===
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===Exercise 4.1:10===
<div class="ovning">
<div class="ovning">
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En 5,4 m lång tvättlina hänger mellan två vertikala träd på 4,8 m avstånd från varandra. Linans ena ände är fäst 0,6 m högre än den andra änden, och 1,2 m från trädet där linan har sin lägre infästning hänger en kavaj på en galge. Bestäm hur mycket under den nedre infästningspunkten som galgen hänger (dvs. avståndet <math>\,x\,</math> i figuren).
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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
 +
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 - Figur - Tvättlina med kavaj på galge}} </center>
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<center> {{:4.1 - Figure - A washing line with a jacket on a hanger}} </center>
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</div>{{#NAVCONTENT:Svar|Svar 4.1:10|Lösning|Lösning 4.1:10}}
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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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