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## Get ready for AP® Calculus

### Unit 1: Lesson 14

Sal converts the degree measures 150° and -45° to radians. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• But why do we keep the pi? can't we do (150*pi)/180=2.6 radians ? or do you need to keep the pi?
• A radian is a relative unit based on the circumference of a circle. As you know, radians are written as a fraction with a π, such as 2π/3, 5π/4, or 3π/2. Since the equation for the circumference of a circle is C=2πr, we have to keep the π to show that it is a portion of the circle. Radian values can be used to calculate arc length using the radian and the radius multiplied together. Since it is encouraged to write these lengths in π units, The symbol is left give a π radian value.
• At , Sal wrote that the circumference is 2pi radii, then at , Sal wrote 2pi radians:
Is a radian equal to the radius. Or is it the same thing, just named differently? I mean, isn't the radian basically the radius bent around on the circumference. I'm really confused right now, so I would really appreciate it if someone would clearly explain this to me... the simpler the explanation, the better :) Thanks in advance!
• You're right about the way you visualize the definition of a radian. It is "the angle subtended by an arc equal in length to the radius." That is, one radian is the angle you would go through if you went one radius-worth of length on the circle. The radius, however, is a length measurement while the radian is an angle measurement.
• On my calculator , I have three angle notations, DRG. I know that D and R are degrees and radians respectively, so I checked on my calculator what it was. It turns out that it was gradians. So I looked it up and realized that a gradian is 10/9 a degree but I couldn't understand what it is used for. Could someone please answer my question? Thanks!
• A gradian is 1/100th of a right angle. It was introduced when France was trying to make everything metric (they had a metric calendar too: it didn't work well). So they took the right angle, the "most natural" angle, and divided it into a hundred parts. So there's 400 gradians to a circle.

• What does a question mean when is says to convert Degrees to Radians in terms of Pi?
• That means not to estimate the value of π, but to leave your answer containing the symbol for π.
For example, 90° in radians is ½π.
• They are different.
Radians is a unit of measure like degrees. 2 pi radians, means you have 2 pi of something and they are radians. It is the same 360 degrees.
A radius is the line from the side of the circle to the center. Sometimes radius refers to the lengh of that line. 2 pi radius means multiply 2 pi by the length of the radius which will give you half of the circumference. It is a length that changes depending on the size of the circle.
• Is there a symbol for radians?
• No. Radians is the ratio the the arc length to the radius, thus the units cancel out, thus there are no units. You can write in "radians" if you like, but it is not required.
• question about radians. so if a radian is equal to about 57 degrees approximately (according to my book) how is the its measurements accurate to a full 360 degree circle?
• There are 2π radians in a full angle (360°)
It is easy to measure angles in radians. All you do is determine the fraction of a circle the angle sweeps out and then multiply that by 2π. For example, a right angle sweeps out ¼ of a circle. So ¼ * 2π = ½π
• Overall, is the radian unit or degree unit used more? Does it vary over different subjects?
• Overall, degrees are used more often, but when you are talking about sin, cos, and tan functions, radians are more common.