RADIAN ANGLE MEASUREMENT

Topics in this lesson:
1. MAKING ANGLES
2. RADIAN ANGLE MEASUREMENT
3. LOCATION OF ANGLES
4. CONVERSION FACTORS FOR CONVERTING ANGLE UNITS
5. APPLICATION OF THE RADIAN ANGLE MEASUREMENT FORMULA
1. MAKING ANGLES
How to make an angle: First, start with a ray ( ). Place another ray on top
of the first. Then rotate the second ray either clockwise or counterclockwise.
Example Animation of an angle being made by rotating counterclockwise.
Example Animation of an angle being made by rotating clockwise.
The measurement of an angle is positive when the angle is made by rotating
counterclockwise and the measurement of an angle is negative when the angle is
made by rotating clockwise.
NOTE: One complete revolution counterclockwise makes the angle 360 . Two
complete revolutions counterclockwise makes the angle 720 . Five complete
revolutions counterclockwise makes the angle 1800 . Ten complete revolutions
clockwise makes the angle 3600 . Thus, there is no largest angle and there is no
smallest angle.
Terminology: The first ray that you start with is the initial side of the angle.
When you stop (or terminate) the rotating of the second ray, this second ray is the
terminal side of the angle. The common point of both rays is the vertex of the
angle.
Copyrighted by James D. Anderson, The University of Toledo
www.math.utoledo.edu/~janders/1330
Initial side of the angle
Terminal side of the angle
Definition An angle is said to be in standard position if the initial side of the angle
is the positive x-axis.
The initial side of the angle above is in the I (quadrant) and the terminal side of
the angle is in the IV (quadrant). Thus, the angle is not in standard position.
NOTE: All the angles that we consider in this class will be in standard position.
When an angle is standard position, we know that the initial side of the angle is the
positive x-axis. So, we only need to be told the location of the terminal side of the
angle. The location of the terminal side of the angle could be I, II, III, IV, the
positive x-axis, the negative x-axis, the positive y-axis, or the negative y-axis.
Since we know that we are talking about the terminal side of the angle, it is
redundant to say the terminal side. Thus, we will say the location of the angle
instead of the location of the terminal side of the angle.