Degrees and radians are two equivalent ways to measure angles. A circle contains 360 degrees, which is equivalent to 2π radians. This means that 360 ° and 2π radians numerically represent the round angle. This means that 180 °, or 1π radians, represents the flat angle. It looks difficult? It is not necessarily. You can easily convert degrees to radians, or vice versa, in a few simple steps. Go to Step 1 to get started.
Steps
Step 1. Write the number of degrees you want to convert to radians
Let's take a couple of examples to better understand the concept. Here are the examples we will work with:
- Example 1: 120°
- Example 2: 30°
- Example 3: 225°
Step 2. Multiply the number of degrees by π / 180
To understand why you need to do this, you should know that 180 equals π radians. Hence, 1 degree is equivalent to (π / 180) radians. Knowing this, you understand why you have to multiply your number of degrees by π / 180 to convert them to radians. You can also remove the degree sign, as they will now be radians. Here's how to do it:
- Example 1: 120 x π / 180
- Example 2: 30 x π / 180
- Example 3: 225 x π / 180
Step 3. Make your calculations
Simply continue with the multiplication by π / 180. Act as if you were multiplying two fractions: the first has the number of degrees in the numerator and "1" in the denominator, and the second has π in the numerator and 180 in the denominator. Here is the detail of the calculations:
- 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 need to express the fraction to the smallest terms to get the final result. Find the greatest common divisor of the numerator and denominator that you will use to simplify the fraction. The highest number for the first example is 60; for the second, it's 30, and for the third, it's 45. But you don't have to just know that; you can proceed by trying to divide both the numerator and denominator by 5, 2, 3, or other appropriate numbers. 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
- Example 3: 225 x π / 180 = 225π / 180 ÷ 45/45 = 5 / 4π radians
Step 5. Write your answer
For clarity, you should write the initial angle measurement that has been converted to radians. Then you are done! Here are the details:
- Example 1: 120 ° = 2 / 3π radians
- Example 2: 30 ° = 1 / 6π radians
- Example 3: 225 ° = 5 / 4π radians
