SMALL CIRCLE
1. Use the Smarties to
measure the radius.
Radius =
MEDIUM CIRCLE
1. Use the Smarties to
measure the radius.
Radius =
LARGE CIRCLE
1. Use the Smarties to
measure the radius.
Radius =
2. Remove the Smarties and
lay them on the circle
where the small circle
intercepts the positive xaxis. Keep in mind that
your Smarties should
“curve” along the arc of
the circle in the positive
direction.
2. Remove the Smarties and
lay them on the circle
where the small circle
intercepts the positive xaxis. Keep in mind that
your Smarties should
“curve” along the arc of
the circle in the positive
direction.
2. Remove the Smarties and
lay them on the circle
where the small circle
intercepts the positive xaxis. 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.
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 small
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 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 small
circle.
5. Remove the Smarties and
continue to the medium
circle.
5. Remove the Smarties and
continue to the large
circle.
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
NUMBER OF
SMARTIES
NUMBER OF RADII
(fraction)
NUMBER OF RADII
(decimal)
Half of the large
circle
Three quarters
of the large circle
The whole circle
What is the term for the length of the distance around the circle?
What is the formula for that measurement?
Using the formula above, if an angle that measures one radian has an arc length of one radius,
one rotation around the entire circle measures how many radians?
Examine the decimal numbers in the last column of the chart. Are any of these numbers
familiar? Why?
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?
Find the radian measure for each of the following angles
0◦ =
90◦ =
180◦ =
270◦ =
360◦ =
Fill in the table below
REFERENCE
ANGLE
REFERENCE
ANGLE
MEASURED IN
RADIANS
QUADRANT
IN WHICH
TERMINAL
SIDE IS
LOCATED
30◦
I
30◦
II
30◦
III
30◦
IV
45◦
I
45◦
II
45◦
III
45◦
IV
60◦
I
60◦
II
60◦
III
60◦
IV
DEGREE MEASURE OF
ANGLE BETWEEN 0 &
360
RADIAN
MEASURE OF
ANGLE