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Degrees <> Radians

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This guide explains the process of converting angles from degrees to radians and vice versa. To convert from degrees to radians, multiply the degree measure by ( frac{pi}{180} ). For example, 150° is equivalent to ( frac{5pi}{6} ) radians. Conversely, to convert from radians to degrees, multiply the radian measure by ( frac{180}{pi} ). For instance, ( frac{11pi}{6} ) radians equals 330°. Additional conversion examples include 210° to ( frac{7pi}{6} ) radians and ( frac{5pi}{4} ) radians to 225°.

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Degrees <> Radians

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  1. Degrees <> Radians

  2. Convert from degrees to radians • Multiply the degree measure by (π/180) • So, 150o = (5 π/ 6) radians because: • 150 (π/180) = 150 π/ 180 • 150/180 reduces to 5/6

  3. Convert from radians to degrees • Multiply the radian measure by (180/ π) • So (11 π/ 6) radians = 330o because: • (11 π/ 6) (180/ π) = (11*180* π) / (6 π) • π cancels • 1980/6 = 330

  4. Convert each measure to radians: • 1) 210o • Answer: (7 π) / 6 • 2) -540o • Answer: -3 π

  5. Convert each measure to degrees • 3) (5 π) / 4 • Answer: 225o • 4) (7 π) / 9 • Answer: 140o

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