Radian Measure On this web page you will investigate using radians to
measure angles. This exploration will reinforce the concepts in Lesson
10.2 of Discovering Advanced Algebra: An Investigative Approach.
Sketch
This sketch gives a dynamic representation of the
definition of radian: a central angle with measure equal to one radian
intercepts an arc that has length equal to the radius of the circle.
Investigate
 Press Rotate Radius to see the radius of
the circle rotate through an angle of 270??
.
 Press Wrap Arc to see the radius of the
circle wrap around an arc of the circle that intercepts an angle of one
radian.
Sketch
This sketch allows you to mark off arcs with measure
equal to one radian on a circle. Press the red X
to hide the arcs and start over.
Investigate
 Press 1 Radian to see an arc of measure
equal to one radian marked off. About how many degrees are in this arc?
 Press Semicircle to mark off a
semicircle with one end at point B. About how many radians
are there in a semicircle?
 Press 1 Circle to mark off a circle
based
at point B. About how many radians are there in a circle?
 Press Go to mark off radians around the
circle clockwise. Press the button again to stop. About how many
radians are there in two full rotations?
Sketch
This sketch shows a central angle along with its
measure in degrees and radians.
Investigate
 Drag point C so that the angle ABC
measures 50??. What is the measure in radians?
 Drag point C so that angle ABC
measures 3.5 radians. What is the measure in degrees?
 Now hide the degree and angle measures. See
if you can move point C so that angle ABC has each
measure below. Press the Show buttons to see how close your
estimate is.
a. 80??
b. 0.5 radians
c. 1 radian
d. 1.5 radians
e. 2 radians
 Write a formula that gives the measure of an
angle in radians if you know its measure in degrees.
 Write a formula that gives the measure of an
angle in degrees if you know its measure in radians.
