Angles and Their Measures



                    

An angle is formed by rotating from the initial side to the terminal side
If the rotation is counterclockwise, the angle formed is a positive angle
If the rotation is clockwise, the angle formed is a negative angle


Angles can be measured in degrees or in radians


                       Degree Measure
Dividing a circles into 360 equal slices, each slice having its vertex
at the center of the circle, the measure of the angle formed by each
slice is one degree


                       Radian Measure
An angle whose vertex coincides with the center of a circle of radius r
and whose terminal and initial sides intersect an arc of length s of the
circumference of the circle, has a measure in radians given by


                      radians                      or                     



            


If     


then

                                      

In other words, one radian is is the size of the central angle of a circle
that intercepts an arc the same length as the radius of the circle

See Examples 1 – 2, pages 416 – 417, of the textbook


                 Conversions

            radians
                                                                                                   



     See Examples 3 – 4, pages 419 – 420, of the textbook


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