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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Acute Angle Domains