596 CHAPTER 6 The Circular Functions and Their Graphs NOTE Another way to convert a radian measure that is a rational multiple of p, such as 9p 4 , to degrees is to substitute 180° for p. In Example 2(a), doing this would give the following. 9p 4 radians = 91180°2 4 = 405° The following table and Figure 4 on the next page give some equivalent angle measures in degrees and radians. Keep in mind that 180° =P radians. Agreement on Angle Measurement Units If no unit of angle measure is specified, then the angle is understood to be measured in radians. For example, Figure 3(a) shows an angle of 30°, and Figure 3(b) shows an angle of 30 (which means 30 radians). An angle with measure 30 radians is coterminal with an angle of approximately 279°. x y 0 308 30 degrees Note the difference between an angle of 30 degrees and an angle of 30 radians. x y 0 30 radians (b) (a) Figure 3 One of the most important facts to remember when working with angles and their measures is summarized in the following statement. Equivalent Angle Measures Degrees Radians Degrees Radians Exact Approximate Exact Approximate 0° 0 0 90° p 2 1.57 30° p 6 0.52 180° p 3.14 45° p 4 0.79 270° 3p 2 4.71 60° p 3 1.05 360° 2p 6.28 These exact values are rational multiples of p.
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