Content

• Steps

Degrees and radians are the two units of the angle. A circle has 360 degrees, which is equivalent to 2π radians, so 360 ° and 2π radians represents the numerical value of the circle "a circle". If you still feel confused then don't worry, with just a few simple steps you can easily convert degrees to radians and vice versa.

Steps

1. 

   Write the number of degrees you want to convert to radians. Let's practice with the following examples so you can understand this concept:
   • Example 1: 120°
   • Example 2: 30°
   • Listing 3: 225°

2. 

   
   
   Multiply the number of degrees by π / 180. To understand why you need to do this, you should know that 180 degrees is equivalent to π radians. Therefore, 1 degree equals (π / 180) radians. From there, what you need to do is multiply the number of degrees you want to convert by π / 180 to convert degrees to radians. The answer is radians so you can remove the degree notation. Here's how:
   • Example 1: 120 x π / 180
   • Example 2: 30 x π / 180
   • Listing 3: 225 x π / 180

3. 

   
   
   Do mathematics. Perform the math by multiplying the number of degrees by π / 180. Similar to multiplying two fractions: the first fraction is the numerator and "1" is the denominator, the second fraction has as the numerator and 180 is the denominator. We do the following:
   • Example 1: 120 x π / 180 = 120π / 180
   • Example 2: 30 x π / 180 = 30π / 180
   • Listing 3: 225 x π / 180 = 225π / 180

4. 

   
   
   Compact. Now you need to put each fraction in its minimal form for the final answer. Find the largest number divisible by both the numerator and the denominator to reduce the fraction. In example 1, the number to look for is 60; in example 2 it is 30 and in example 3 is 45. But don't rush; You can try first by dividing the numerator and denominator by 5, 2, 3, or any other usable number. Here's how to 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
   • Listing 3: 225 x π / 180 = 225π / 180 ÷ 45/45 = 5 / 4π radians

5. 

   Write your answer. To complete the math explicitly, you can write the original angle measure output when converted to radians. Proceed as follows:
   • Example 1: 120 ° = 2 / 3π radians
   • Example 2: 30 ° = 1 / 6π radians
   • Listing 3: 225 ° = 5 / 4π radians
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