2.2: Conversion between Degrees and Radians
You are hard at work in the school science lab when your teacher asks you to turn a knob on a detector you are using
Read this Concept, and at the conclusion you'll be able to accomplish this task and turn the knob the appropriate amount.
Watch This
James Sousa Example: Converting Angles in Degree Measure to Radian Measure
Guidance
Since degrees and radians are different ways of measuring the distance moved around the circumference of a circle, it is reasonable to suppose that there is a conversion formula between these two units. This formula works for all degrees and radians. Remember that:
If we have a degree measure and wish to convert it to radians, then manipulating the equation above gives:
Example A
Convert
From the last section, you should recognize that this angle is a multiple of
Here is what it would look like using the formula:
Example B
Convert
and reducing to lowest terms gives us
You could also have noticed that 120 is
Example C
Express
Note: Sometimes students have trouble remembering if it is
Vocabulary
Radian: A radian (abbreviated rad) is the angle created by bending the radius length around the arc of a circle.
Degree: A degree is a unit for measuring angles in a circle. There are 360 of them in a circle.
Guided Practice
1. Convert the following degree measures to radians. All answers should be in terms of
2.Convert the following degree measures to radians. All answers should be in terms of
3. Convert the following radian measures to degrees
Solutions:
1.
2.
3.
Concept Problem Solution
Since you now know that the conversion for a measurement in degrees to radians is
you can find the solution to convert
Practice
Convert the following degree measures to radians. All answers should be in terms of

90∘ 
360∘ 
50∘ 
110∘ 
495∘ 
−85∘ 
−120∘
Convert the following radian measures to degrees.

5π12 
3π5 
8π15 
7π10 
5π2 
3π 
7π2  Why do you think there are two different ways to measure angles? When do you think it might be more convenient to use radians than degrees?
Notes/Highlights Having trouble? Report an issue.
Color  Highlighted Text  Notes  

Please Sign In to create your own Highlights / Notes  
Show More 
Degree
A degree is a unit for measuring angles in a circle. There are 360 degrees in a circle.radian
A radian is a unit of angle that is equal to the angle created at the center of a circle whose arc is equal in length to the radius.subtended arc
A subtended arc is the part of the circle in between the two rays that make the central angle.Image Attributions
Here you'll learn how to convert degrees to radians, and vice versa.