Degrees and radians are two units for measuring angles. A circle has 360 degrees, which is equal to 2π radians, so 360 ° and 2π radians represent the numerical value of "one turn" of a circle. Does it seem confusing? Don't worry as you can convert degrees to radians or radians to degrees with a few very simple steps.
Steps
Step 1. Write the number of degrees you want to convert to radians
Here are some examples for you to understand well:
- Example 1: 120°
- Example 2: 30°
- Example 3: 225°
Step 2. Multiply the degrees by π / 180
To understand why you should do this calculation, you have to know that 180 ° equals 1π radian. So 1 degree equals (π / 180) radians. Now that you know this, multiply the degrees by π / 180 to convert degrees to radians. You can remove the degrees symbol, since you will express the result in radians. This is the way to do it:
- Example 1: 120 x π / 180
- Example 2: 30 x π / 180
- Example 3: 225 x π / 180
Step 3. Perform the calculation
Multiply the degrees by π / 180. Think of it like multiplying two fractions: the first fraction has degrees as the numerator and "1" as the denominator, while the second fraction has π as the numerator and 180 as the denominator. This is how you should do the calculation:
- Example 1: 120 x π / 180 = 120π / 180
- Example 2: 30 x π / 180 = 30π / 180
- Example 3: 225 x π / 180 = 225π / 180
Step 4. Simplify
Now you have to reduce the fraction to the minimum to get the final result. Find the largest number that can be divided evenly between the numerator and denominator of each fraction, and simplify. The largest number for Example 1 is 60; for the second, 30; and for the third, 45. You don't need to know this number all at once. You can try dividing the numerator and denominator by 5, 2, 3, or any number that is a divisor of both numbers. This is how you should do it:
- Example 1: 120 x π / 180 = 120π / 180 ÷ 60/60 = 2 / 3π radians
- Example 2: 30 x π / 180 = 30π / 180 ÷ 30/30 = 1 / 6π radians
- Example 3: 225 x π / 180 = 225π / 180 ÷ 45/45 = 5 / 4π radians
Step 5. Write the answer
To avoid mistakes, write the angle measure in radians. You finished! This is how you should do it:
- Example 1: 120 ° = 2 / 3π radians
- Example 2: 30 ° = 1 / 6π radians
- Example 3: 225 ° = 5 / 4π radians