Radian Measure

 

Definition: The Radian Measure of an Angle

Place the vertex of the angle at the center of a circle of radius r. Let a denote the length of the arc intercepted by the angle, as indicated in Figure 1 of the text. Page A24.  The radian measure  of the angle is the ratio of the arc length a to the radius r.  In symbols,

 

                                               

In this definition, it is assumed that a and r have the same linear units.

 

 

 

Converting from radian measure to degrees and vice-versa:

 

Important Relationship:  radians. (Recall )

 

Hence:  radians          and       1 radian = . (1 radian )

 

We use the above to help us convert from degrees to radians and radians to degrees.

 

To convert from degrees to radians, multiply by .  To convert from radians to degrees, multiply by .

 

Examples

  1. Convert  to radian measure.
  2. Convert  to degree measure.

 

Table1 Revised

1

 

 

 

ONE OPTION:

Three step procedure for evaluating trigonometric functions for either degrees or radians.

 

  1. Draw the angle and then the triangle on the coordinate axis. (See figure 10, page A27)
  2. Determine the reference angle if necessary.
  3. Evaluate the value of the trigonometric function at the reference angle, keeping in mind if the evaluation should be positive or negative.  (To check yourself, remember the ASTC in figure 9 on page A27.)

 

Example – Evaluate each of the following:

1.

2.

3.

4.

5.

6.