Content

• Steps

Radians and degrees are two units of measure for angles. The full angle (or circle) is 360 °, which is equivalent to 2π radians; both values ​​represent one “turn in a circle”. Therefore, a half-turn is equal to 1π radians or 180 °. Confused? Then read this article and learn how to convert degrees to radians.

Steps

1. 1 Write down the degrees you want to convert to radians.
   • Example 1: 120 °
   • Example 2: 30 °
   • Example 3: 225 °
2. 2 Multiply degrees by π / 180. Explanation of this factor: Since 180 ° = π radians, then 1 ° = π / 180 radians. When multiplying, get rid of the sign of the degrees, since the answer will be written in radians.
   • Example 1: 120 x π / 180
   • Example 2: 30 x π / 180
   • Example 3: 225 x π / 180
3. 3 Calculate radians. To do this, multiply the degrees by π and write the result in the numerator, and leave 180 in the denominator.
   • Example 1: 120 x π / 180 = 120π / 180
   • Example 2: 30 x π / 180 = 30π / 180
   • Example 3: 225 x π / 180 = 225π / 180
4. 4 Simplify the resulting fraction. To do this, divide both the numerator and the denominator by their greatest common factor (GCD is the largest number by which both the numerator and the denominator are integer divisible). In the first example, GCD = 60; in the second it is 30; in the third it is 45. If you cannot find the GCD quickly, divide the numerator and denominator by 2, 3, 4, 5 or other suitable numbers. Here's how to do it:
   • Example 1: 120 x π / 180 = 120π / 180 ÷ 60/60 = 2π / 3 radians
   • Example 2: 30 x π / 180 = 30π / 180 ÷ 30/30 = 1π / 6 radians
   • Example 3: 225 x π / 180 = 225π / 180 ÷ 45/45 = 5π / 4 radians
5. 5 Write down your answer.
   • Example 1: 120 ° = 2π / 3 radians
   • Example 2: 30 ° = 1π / 6 radians
   • Example 3: 225 ° = 5π / 4 radians