Content

• To step
• Tips
• Necessities

Radians and degrees are both units of measurement for angles. As you may know, a circle can be divided into 2π radians, the equivalent of 360 °; both values ​​represent a "revolution" of a circle. Therefore, 1π radians is the same as 180 ° degrees in a circle, making 180 / π the perfect conversion tool for converting radians to degrees. To convert a number from radians to degrees, simply multiply the value of the radian by 180 / π. If you want to know how to do this and how to understand the concept of this procedure, read on to Step 1 to get started.

To step

1. Know that π radians equals 180 degrees. Before starting the conversion, you need to know that π radians = 180 °, which is equal to a semicircle. This is important because you will be using 180 / π as the conversion unit. This is because 1π radians equals 180 / π degrees.
2. Multiply the radians by 180 / π to convert to degrees. It's that simple. Suppose you are working with π / 12 radians. Then you have to multiply this by 180 / π and simplify if necessary. This is done as follows:
   • π / 12 x 180 / π =
   • 180π/12π ÷ 12π/12π =
   • 15°
   • π / 12 radians = 15 °
3. Practice this with a few examples. If you really want to get the hang of it, try converting radians to degrees with a few additional examples. Here are a few other exercises you can work through:
   • 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. Remember that there is a difference between "radians" and "" radians ". When we talk about 2π radians or 2 radians, these are two different terms. As you know, 2π radians equals 360 degrees, but if you are dealing with 2 radians, if you want to convert this to degrees, you will have to calculate 2 x 180 / π. You then get 360 / π, or 114.5 °. This is a different answer, because if you are not working with π radians, the π cannot be crossed out in the equation, resulting in a different value.

Tips

• When multiplying, leave the pi in your radians as a symbol, and not the decimal approximation, so that you can more easily cross it out during a calculation.
• Many graphing calculators have unit conversion functions or you can use them to download programs that do this. Ask your math teacher if your calculator has such a feature.

Necessities

• Pen or pencil
• Paper
• Calculator