8-29-14
T1.2g To Find Arc Length And Area Of A Sector
A medicine wheel in Wyoming, used for religious
and ceremonial events. There are 32 spokes. 1
OPENER: If a bicycle wheel revolves 75 times every
minute, through how many degrees will it move in a 2
hour period?
75 r.
360

1 min.
1 r.
60 min.
1,620,000


1 hr.
1 hr.
1,620,000 2 hr.
 3,240,000

1
1 hr.
The wheel moves 3,240,000° in a 2 hour period.
2
OPENER # 2
What are the reference angles for the following?
1. 71°
2. 219°
3. 158°
4. 296°
1. 71°
2. 39°
3. 22°
4. 64°
90°
0°
180°
360°
270°
Thurs 9/4: Quiz on
•Reference Angles
•Rotation
•Arc length
•Sector area
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Active Learning Assignment?
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LESSON: The Arc Length on a circle is the part of the
circumference that is between the initial and terminal sides of
an angle. To find the Arc Length, what could be important?
These two circles are the same size. The red and
blue curves represent the arcs.
Are the arcs the same size? What makes the difference?
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Ah ha! The angle is important. What if we have the
same angle on two different circles?
Are the arcs the same size? What makes the difference
here?
67°
67°
So, the radius makes a difference, too. It there anything
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else that could influence the size of the arc?
What are the relationships between the angle size,
radius length, and the arc length?
Since it is a direct variation, that is, the larger the angle, the
larger the arc and the larger the radius, the larger the arc, then
we have the formula for ARC LENGTH of that sector:
*
Arc length
Radius
s = rӨ (Ө is always in radians)
Angle
What if we’re given
degrees? Convert it!
Use

180
or
180

?
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Using the formula s = rӨ, try: (1 decimal place)
1. The sector of a circle has a radius of 4 cm and a central
angle is 2.4. What is the length of the arc?
?
2.4
4 cm
s = rӨ
s   4cm  2.4 
 9.6 cm.
The length
is 9.6 cm.
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Try:
2. The sector of a circle has a radius of 8 m and an angle is
48°. What is the length of the arc? (1 decimal place)
s = rӨ
?
  
s  8m  48  

The length
 180 
is 6.7m.
 6.7 m.
8 * 48 * π / 180
3. If an arc is 12 inches and the radius of a circle is 5 inches,
what is the angle? What is the degree measurement?
The angle
12in
s = rӨ
    2.4
is 2.4.
5in
12in   5in  
 180   137.5
The angle
2.4 

is 137.5°. 9
  
The Sector Area of a circle is the part of the circle that is
between the initial and terminal sides of an angle. The same
factors that influence the arc length influence the sector area.
1 2
K r 
2
*
Area
Radius
1 2
The formula is : K  r 
2 Angle
( is always in radians.)
Try:
A sector of a circle has a radius of 3 inches and a central angle
of 27°. Find the sector area to one decimal place.
?
1 2
 

2
K   3  27  
.5

3
 27   / 180

2
 180 
The sector area is 2.1 in.2
= 2.1
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The medicine wheel has a radius of 30 feet, with 32 sectors.
We want to know the arc length and the sector area.
1. First, we need to find
the angle measure of
each sector.

2


32
16
2. Find the arc length of
each sector. (1 dec. pl.)
s = rӨ
 
s  30ft  
 16 
= 5.9 ft
3. Find the sector area. (1 dec. pl.)
1 2
K r 
2
1
2  
K   30ft    = 88.4 ft2
2
 16 
The arc length is 5.9 ft and the sector area is 88.4 ft2.
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Active Learning Assignment:
Written Exercises P 264: 1 – 8
(ALWAYS WRITTEN, UNLESS DIRECTED
OTHERWISE)
Thursday 9/4: Quiz on
•Reference Angles
•Rotation
•Arc length
•Sector area
•Review on Weebly
How do you study for a math test or quiz?
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