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This video is provided as supplementary material
for courses taught at Howard Community College and in this video
I want to show how to convert between degrees and radians,
and it's really a very simple process. To understand the process,
all we have to do is remember that a circle
can be measured in degrees, that's 360 degrees,
or it could be measured in radians, and a circle in radians
is 2 pi. Given that fact,
a semi-circle, a half a circle, would have half as many degrees.
It would have 180 degrees,
or it would have just pi as its radian measure.
Now let's take that information and figure out how to convert
30 degrees into radians.
So what I'm going to do is take these two numbers, 180 degrees
and pi, and make a fraction. If they
equal each other, and one number is the numerator
and the other is the denominator, the fraction will equal 1.
So I'm gong to make the fraction
pi over 180 degrees.
Now what happens when I do this, when I multiply,
is the degree signs cancel out.
I've got a 30 in the numerator over here
and 180 down here in the denominator. I can simplify this.
I can divide both numbers by 30. I get a 1,
and the 180 divided by 30 is just...
let's see... That's 6. So I get
pi over 6 as the radian measure
that's equivalent to 30 degrees.
Okay, let's do one more degrees into radians.
This is not quite as nice a number, 17 degrees.
I'll use the same process. I'm multiply that by
pi over 180 degrees.
I can cancel the degrees, but I can't simplify the 17 and the 180.
So I just multiply 17 pi
over 180.
And this is the radian measure. What I probably want to do with this
is put that number into the calculator and get it
as a decimal, which would also be radians. So that's how
you convert
from degrees to radians. you multiply by the fraction pi
over 180 degrees. Now to convert
radians to degrees we use basically the same idea.
Let's say we have
pi over 12 and want to convert that to degrees.
I'll just take the fraction I used before and flip it over.
It'll still be equal to 1. So I'm gonna have a 180 degrees
over pi. When I multiply, the first thing I see is
pi cancels. I've got a 180 degrees in the numerator
and 12 in the denominator. I can divide both of these numbers by 12.
That puts a 1 down here in the denominator, and 12
into 180 is 15. So that's going to be
15. I've still got the degree sign,
so my answer is 15 degrees.
And let's do one more.
So let's say I start out with 2.5
as my radian measure. I multiply that by
180 degrees over pi.
There's not much I can do in terms of simplifying this,
so I just multiply across. 2.5 times 180 degrees...
that's going to get me
450 degrees divided by pi.
And then I'll put this into a calculator and
find what the decimal number is that this ,equals
and that once again will be a degree measure.
So that's basically the whole process. If you're going from
degrees to radians, you're going to use pi over 180
for the fraction that you multiply by.
If you're going from radians to degrees, you'll flip that fraction
and use 180 degrees
over pi. That's it. Take care.
I'll see you next time.