This leads to the conversion factors. One way to convert from degrees to radians is take the number of degrees and multiply it by this conversion factor, pi over , multiplied by pi over and you'll get your radians. To get from radians to degrees, you multiply by this conversion factor times over pi and we'll use those conversion factors in a second. One thing I want to talk about here is in advanced Math, we tend to think of angles as rotations of a ray about a point, so when you look at the initial side and the terminal side of an angle, imagine the initial side has rotated around to the terminal side and that kind of thinking allows us to envision angles like degrees which is greater than one revolution.
It also allows us to think about negative angles like this one -3 pi over 4, the initial side has rotated clockwise 3 pi over 4. In Mathematics, the clockwise direction is defined as negative, counter clockwise is positive, that's really important.
Now you will notice that in both of these cases I drew the angles superimposed on the coordinate system with the vertex right at the origin and the initial side on the positive x axis, this is called standard position and this is the way we're going to be drawing angles for the rest of the course, but you'll see this a lot in any Pre-calculus course.
These are angles drawn in standard position. Let's convert each of these to the other form of measure, this one is in degrees, so I want to convert it into radians.
I can use my conversion factor here degrees times pi over Now there's a lot of common factors here, this is 30 times 6, this is 30 times 13 and the 30s can cancel and you're left with 13 pi over 6. In this case we've got -3 pi over 4, we want to convert these to degrees, so -3 pi over 4. We want to multiply by over pi, degrees over pi. Remember in the conversion factor if you have a hard time remembering which is which, when the degrees are in the numerator, your answer is going to be in degree.
When your degrees are in the denominator, your answers are going to be in radians. So here I just want to cancel the pi's, 4 cancels with leaving 45 and -3 times 45 is degrees. So you don't have to use the conversion factors to convert from degrees to radians, you could always use this fact, but the conversion factors are handy for people who like formulas. And also don't forget, the measure of angle in standard position, this is the way we'll draw angles from now on.
Why exactly that number, not some other? Also, does this work only for unit circle, or for any circle? We simplify by dividing by two. Think of it as solving proportions. The radian is defined as the plane angle subtended by any circular arc divided by its radius. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
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Active Oldest Votes. JustKitten JustKitten 68 4 4 bronze badges. Check out my comment on the gtb's answer. Unless the unit definitions were changed ie.
It's the ratios that matter. I guess I can't understand why because I don't know how a radian is defined, but I'll look it up.
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