SMALL CIRCLE
1. Use the Smarties to measure the
radius.
Radius =
smarties
2. Use those smarties to measure
an arc. The arc should start at
the intersection of the small
circle and the positive x-axis.
Use only as many smarties as
you used to measure the radius.
Keep in mind that your Smarties
should “curve” along the arc of
the circle in the positive
direction.
3. Make a mark on the circle where
the last Smarty ends. Remove
the Smarties and draw a ray
from the origin through the
mark.
4. Examine the central angle
formed by the line you just drew
and the positive x-axis. This
central angle intercepts an arc
whose length is equal to the
of the
small circle.
5. Remove the Smarties and
continue to the medium circle.
MEDIUM CIRCLE
1. Use the Smarties to measure the
radius.
Radius =
smarties
LARGE CIRCLE
1. Use the Smarties to measure the
radius.
Radius =
smarties
2. Use those smarties to measure
an arc. The arc should start at
the intersection of the medium
circle and the positive x-axis.
Keep in mind that your Smarties
should “curve” along the arc of
the circle in the positive
direction.
2. Use those smarties to measure
an arc. The arc should start at
the intersection of the large
circle and the positive x-axis.
Keep in mind that your Smarties
should “curve” along the arc of
the circle in the positive
direction.
3. Make a mark on the circle where
the last Smartie ends. Remove
the Smarties and draw a ray
from the origin through the
mark.
3. Make a mark on the circle where
the last Smartie ends. Remove
the Smarties and draw a ray
from the origin through the
mark.
4. Examine the central angle
formed by the line you just drew
and the positive x-axis. This
central angle intercepts an arc
whose length is equal to the
of the medium
circle.
4. Examine the central angle
formed by the line you just drew
and the positive x-axis. This
central angle intercepts an arc
whose length is equal to the
of the large
circle.
5. Remove the Smarties and
continue to the large circle.
Check in with your teacher
NAME
REFLECTION- Before you leave the room, write down any questions that you have and at least two things that
you learned today. Return this sheet to me.
QUESTIONS
TODAY I LEARNED
GEOMETRY VOCABULARY
Perimeter is to triangle as
is to circle.
Side length is to perimeter as
is to
The formula for the
of a circle is
The measure of the central angle (the angle formed by the line from the center of the circle to the edge of the
circle and the positive x-axis) you drew in each of the circles is called one radian.
Using only the large circle and Smarties fill out the chart below. Remember, one radius on the large circle
measures
Smarties.
ARC
MEASUREMENT
Quarter of the
large circle
Half of the large
circle
Three quarters
of the large circle
The whole circle
NUMBER OF
SMARTIES
NUMBER OF RADII
(fraction)
NUMBER OF RADII
(decimal)
Examine the decimal numbers in the last column of the chart. Are any of these numbers familiar? Why?
DEFINITION-RADIAN MEASURE
Using the definition above, what conclusion can you draw about angle measure (in radians) and arc length if
the circle intercepted by the angle has a radius equal to one unit.
Using the formula for circumference and the definition of radian measure, find the measure (in radians) for an
angle that represents one rotation around the entire circle?
How does this compare to
the chart above? Use these ideas to fill in the chart on the following page.
Given a circle that has a radius equal to 1, fill in the chart below.
DESCRIPTION OF
ARC
EXACT ARC
LENGTH
(no decimals)
EXACT ANGLE
MEASURE IN
RADIANS
EXACT ANGLE
MEASURE IN DEGREES
The Entire Circle
¾ of the Circle
½ of the circle
¼ of the circle
If given an angle measured in degrees, how would you convert it to radians?
If given an angle measured in radians, how would you convert it to degrees?