595 6.1 Radian Measure We can use the relationship 180° = p radians to develop a method for converting between degrees and radians as follows. 180° =P radians Degree / radian relationship 1° = P 180 radian Divide by 180. or 1 radian = 180° P Divide by p. Converting between Degrees and Radians • Multiply a degree measure by p 180 radian and simplify to convert to radians. • Multiply a radian measure by 180° p and simplify to convert to degrees. EXAMPLE 1 Converting Degrees to Radians Convert each degree measure to radians. (a) 45° (b) -270° (c) 249.8° SOLUTION (a) 45° = 45a p 180 radianb = p 4 radian Multiply by p 180 radian. (b) -270° = -270a p 180 radianb = - 3p 2 radians Multiply by p 180 radian. Write in lowest terms. (c) 249.8° = 249.8a p 180 radianb ≈4.360 radians Nearest thousandth S Now Try Exercises 11, 17, and 45. This radian mode screen shows TI-84 Plus conversions for Example 1. Verify that the first two results are approximations for the exact values of p 4 and - 3p 2 . EXAMPLE 2 Converting Radians to Degrees Convert each radian measure to degrees. (a) 9p 4 (b) - 5p 6 (c) 4.25 SOLUTION (a) 9p 4 radians = 9p 4 a 180° p b = 405° Multiply by 180° p . (b) - 5p 6 radians = - 5p 6 a 180° p b = -150° Multiply by 180° p . (c) 4.25 radians = 4.25a 180° p b ≈243.5°, or 243° 30′ 0.50706160′2 ≈30′ S Now Try Exercises 29, 33, and 57. This degree mode screen shows how a TI-84 Plus calculator converts the radian measures in Example 2 to degree measures. NOTE Replacing p with its approximate integer value 3 in the fractions above and simplifying gives a couple of facts to help recall the relationship between degrees and radians. Remember that these are only approximations. 1° ≈ 1 60 radian and 1 radian ≈60°
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