Converting between degrees and radians

Converting between degrees and radians is pretty easy.

To convert radians to degrees, multiply by 180° and divide by ∏.

To convert degrees to radians, divide by 180° and multiply by ∏.

In my opinion, the easiest way to remember this is to think of it as canceling out. Meaning, if you start with degrees, you need to cancel out the degrees, thus you have to divide by degrees (180). If you start with radians, you need to cancel out radians, thus you have to divide by radians (∏).

Let's try a few examples:

1) Convert 90° to radians.

90°/180° = ½

½ · ∏ = ∏/2 radians

Normally it is best to leave the answer with ∏ because that is exact.
So our answer is ∏/2 radians.

Occasionally, however, you may need to get a numerical answer,
in which case you just need to divide ∏ by 2 to get approximately 1.57 radians.

2) Convert 52° to radians.

52°/180° = 13/45

13/45 · ∏ = 13∏/45 radians

This answer is exact, but let's also get an approximation: 0.908 radians.

3) Convert ∏/4 radians to degrees.

∏/4 ÷ ∏ = ¼

¼ · 180°=45°

4) Convert 3.8 radians to degrees.

3.8 ÷ ∏ = 1.2095....

1.2095 · 180° = 217.7°

Practice: Convert the following. Give an exact answer when possible as well as an approximation rounded to the tenths place.

1) Convert 75° to radians.

2) Convert 200° to radians

3) Convert 312° to radians

4) Convert 3∏/4 radians to degrees

5) Convert 7∏/5 radians to degrees

6) Convert 1.35 radians to degrees

Answers: 1) 5∏/12 = 1.3 radians   2) 10∏/9 = 3.5 radians    3) 26∏/15 = 5.4 radians    4) 135°    5) 252°    6) 77.3°

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