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Radians and degrees are two units of measure for angles. The total angle (or circle) is 2π radians, which is equivalent to 360 °; both values ​​represent one “turn in a circle”. Therefore, a half-turn is equal to 1π radians or 180 °; thus 180 / π is the ideal multiplier for converting radians to degrees. To convert radians to degrees, simply multiply the given value in radians by 180 / π.

Steps

1. 1 1π radians equals 180 degrees. This is important because you will be using a multiplier of 180 / π for the conversion.
2. 2 To convert radians to degrees, multiply the given value in radians by 180 / π. It’s very simple. For example, you are given an angle equal to π / 12 radians. Multiply this value by 180 / π and simplify the result (if necessary). Here's how to do it:
   • π / 12 x 180 / π =
   • 180π/12π ÷ 12π/12π =
   • 15°
   • π / 12 radians = 15 °
3. 3 Practice converting. If you want to learn how to quickly convert radians to degrees, practice it. Here are some examples:
   • Example 1: 1 / 3π radians = π / 3 x 180 / π = 180π / 3π ÷ 3π / 3π = 60 °
   • Example 2: 7 / 4π radians = 7π / 4 x 180 / π = 1260π / 4π ÷ 4π / 4π = 315 °
   • Example 3: 1 / 2π radians = π / 2 x 180 / π = 180π / 2π ÷ 2π / 2π = 90 °
4. 4 Remember: there is a difference between "radians" and "π radians". 2π radians and 2 radians are not the same thing. As you know, 2π radians equals 360 degrees, but if you want to convert 2 radians, then do it like this: 2 x 180 / π. You get 360 / π or 114.5 °. This is a different result, because if you are not working with “π radians,” then π is not canceled in the calculation, which leads to different values.

Tips

• When converting, write pi as a character, not as a decimal number. In this case, you will simplify the calculations, since pi will shrink.
• Many graphing calculators can convert units of measurement, or just download a converter program.

What do you need

• Pen or pencil
• Paper
• Calculator