Radians and degrees are both units of measurement used in measuring angles. As you know, a circle is made up of 2π radians, equivalent to 360 °; both of these values represent a complete "turn" on the circumference of the circle. Therefore, 1π radians correspond to 180 ° of the circle, which makes the 180 / π ratio the ideal conversion tool for converting radians to degrees. To convert radians to degrees, simply multiply the radian value by 180 / π. If you want to know how to calculate this conversion and understand the concept behind the process, start reading Step 1.
Steps
Step 1. Understand that π radians equals 180 degrees
Before starting the conversion process, it is important to know that π radians = 180 °, this is equivalent to half a turn on the circle. This is important because you will be using 180 / π as your conversion metric.
Step 2. To convert to degrees, multiply the radians by 180 / π
The process is really simple. Let's assume you are working with π / 12 radians. You will need to multiply π / 12 radians by 180 / π and, when necessary, simplify the result. Here's how to proceed:
- π / 12 x 180 / π =
- 180π / 12π ÷ 12π / 12π =
- 15°
- π / 12 radians = 15 °
Step 3. Practice some examples
If you really want to become familiar with this type of operation, try a few exercises to calculate the conversion from radians to degrees. Here are some problems you can try to solve:
- Example 1: = 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 °
Step 4. Remember that there is a difference between "radians" and "π radians"
When we talk about 2π radians or 2 radians, the same terms are not used. As you well know, 2π radians are equal to 360 °, but if you are operating with 2 radians and wish to convert them to degrees, you will have to perform the following calculation: 2 x 180 / π. You will get 360 / π, or 114.5 °. This is a different result, because if you are not operating with π radians, the π will not be canceled out in the equation and the operation will result in a different value.
Advice
- During multiplication, keep the π symbol of your radians instead of using the value in decimal form, this way you can clear it more easily during the operation.
- Many calculators have some functions for converting units of measurement, but you can also download special programs. Ask your math teacher if this function is present on your calculator.
