circular measure

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Circular Circular measure measure Area of a Circle Definition of radians Click on a topic Area of a Sector Exit Exit Definition of

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Page 1: Circular Measure

Circular measureCircular measure

Area of a CircleDefinition of radians

Click on a topic

Area of a Sector

ExitExit

Definition of

Page 2: Circular Measure

Definition of

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(Pi)

nextnext

Page 3: Circular Measure

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Take any size of circle.

Page 4: Circular Measure

d

C

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C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

Page 5: Circular Measure

d

C

ExitExitbackbackPage 1Page 1 nextnext

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

Page 6: Circular Measure

d

C

ExitExitbackbackPage 1Page 1 nextnext

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

Page 7: Circular Measure

C

d

ExitExitbackbackPage 1Page 1 nextnext

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

Page 8: Circular Measure

C

d

ExitExitbackbackPage 1Page 1 nextnext

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

Page 9: Circular Measure

C

d

ExitExitbackbackPage 1Page 1 nextnext

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

Page 10: Circular Measure

C

d

is about 3 times

ExitExitbackbackPage 1Page 1 nextnext

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

dC

Page 11: Circular Measure

C

d

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This is true for any size of circle

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

dC = 3.1415927 x

Page 12: Circular Measure

C

d

ExitExitbackbackPage 1Page 1 nextnext

This number is called (pi)

This is true for any size of circle

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

dC = x

dC = 3.1415927 x

Page 13: Circular Measure

C

d

dC = x

= 3.1415927

dC = 3.1415927 x

This number is called (pi)

This is true for any size of circle

C is the Circumference, the distance around the outside.

d is the Diameter.

Take any size of circle.

ExitExitbackbackPage 1Page 1 nextnext

Page 14: Circular Measure

Definition

ExitExit

S Sr

radians

r

11ccDefinitionDefinition 22cc

Page 1Page 1

33cc 44cc 55cc 66cc 1 revolution1 revolution

cc means circular measure i.e. radians means circular measure i.e. radians

Page 15: Circular Measure

Definition

ExitExit

= 1radian

11ccDefinitionDefinition

S = r

Sr

radians

r

22cc

Page 1Page 1

33cc 44cc 55cc 66cc 1 revolution1 revolution

cc means circular measure i.e. radians means circular measure i.e. radians

Page 16: Circular Measure

Definition

ExitExit

= 2 radians

11cc 22ccDefinitionDefinition

S = 2r

Sr

radians

r

Page 1Page 1

33cc 44cc 55cc 66cc 1 revolution1 revolution

cc means circular measure i.e. radians means circular measure i.e. radians

Page 17: Circular Measure

Definition

ExitExit

= 3 radians

11cc 22cc 33ccDefinitionDefinition

S = 3r

Sr

radians

r

Page 1Page 1

44cc 55cc 66cc 1 revolution1 revolution

cc means circular measure i.e. radians means circular measure i.e. radians

Page 18: Circular Measure

Definition

ExitExit

= 4 radians

11cc 22cc 33cc 44ccDefinitionDefinition

S = 4r

Sr

radians

r

Page 1Page 1

55cc 66cc 1 revolution1 revolution

cc means circular measure i.e. radians means circular measure i.e. radians

Page 19: Circular Measure

Definition

ExitExit

= 5 radians

11cc 22cc 33cc 44cc 55ccDefinitionDefinition

S = 5r

Sr

radians

r

Page 1Page 1

66cc 1 revolution1 revolution

cc means circular measure i.e. radians means circular measure i.e. radians

Page 20: Circular Measure

Definition

ExitExit

= 6 radians

11cc 22cc 33cc 44cc 55cc 66ccDefinitionDefinition

S = 6r Sr

radians

r

Page 1Page 1

1 revolution1 revolution

cc means circular measure i.e. radians means circular measure i.e. radians

Page 21: Circular Measure

Definition

ExitExit

= 2 radians

11cc 22cc 33cc 44cc 55cc 66cc 1 revolution1 revolutionDefinitionDefinition

S = 2r

Sr

radians

r

Page 1Page 1

cc means circular measure i.e. radians means circular measure i.e. radians

Page 22: Circular Measure

Area of a circle

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Show dimensionsShow dimensions

Page 23: Circular Measure

Area of a circle

Cut into sectorsCut into sectors

r

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C =2 r

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Page 24: Circular Measure

Area of a circle

ExitExitbackback

C =2 r

r

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Open outOpen out

Page 25: Circular Measure

C 2

r

= r

Area of a circleC =2 r

C 2

= r

ExitExitbackbackPage 1Page 1

Push togetherPush together

Page 26: Circular Measure

Area of a circleC =2 r

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Area of rectangleArea of rectangle

r

r

Page 27: Circular Measure

r

r

Area = r2

Area of a circleC =2 r

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Page 28: Circular Measure

Area of a sector

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Show dimensionsShow dimensions

Page 29: Circular Measure

Cut into small sectorsCut into small sectors

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Area of a sector

S = rr

Page 30: Circular Measure

ExitExitbackbackPage 1Page 1

Open outOpen out

Area of a sector

S = rr

Page 31: Circular Measure

ExitExitbackbackPage 1Page 1

Open outOpen out

Area of a sectorr2

r2

r

Page 32: Circular Measure

r

ExitExitbackbackPage 1Page 1

Push togetherPush together

Area of a sectorr2

r2

Page 33: Circular Measure

r

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Area of a sector

r2

Area of rectangleArea of rectangle

Page 34: Circular Measure

Area = ½ r2

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Area of a sector

r

r2