>> Julie Harland:
This is your math gal,
Julie Harland.
Please visit my website
at yourmathgal dot com
where all of my videos are
organized by topic.
This is Part Four
of radian measure of angles,
and in this video,
we do one conversion.
We convert one radian
to two degrees.
We want to find
out what one radian is
if it's converted to degrees.
And then starting
in Part Five, we do a lot
of different conversions,
going from degree measures
to radians
or from radian measure
to degree measure.
What is the degree measure
of one radian?
That's the same thing
as somebody saying one radian
equals how many degrees, and,
remember, we don't have
to write radian.
We can just say one equals.
Alright. So now we have
to remember how we
define radians.
So we have
to have some angle here,
and the radian measure is the
length of the arc divided
by the radius.
So in order for the length
of the arc, wherever it is,
I'm not sure where s is going
to be, it's somewhere up here,
so that when I divide s over r
to get 1, what is that going
to tell me?
If s over r is equal to 1,
that means that s has
to be the same length as r.
So what we want is to make
about the same length here
as r. OK.
So, in other words,
this is actually the number r.
So you can look at it
and guess, well, gosh,
what does it look like?
It looks like it's less
than 90 degrees.
It looks like maybe it's more
than 45 degrees,
etc. So let's see what it
is exactly.
So we're going to use the idea
that pi is the same thing
as 180 degrees.
So I'm starting off, now,
with the number 1, OK,
and I want to get the answer
in degrees.
So I want to multiply it
by something so I get degrees
in the numerator.
So I can even multiply
by 180 degrees over pi or pi
over 180 degrees
because since those are the
same number,
when you divide one
by the other,
it's like one [inaudible]
by one.
So if I multiply it
by 180 degrees over pi,
I am now going
to have my answer in degrees.
So what's that mean?
That means 100, I'm sorry.
That means
that one radian here is
exactly 180 degrees over pi,
or I write it like this.
Even better.
It's 180 over pi degrees.
So this is the exact answer
right here.
Now let's go ahead
and round that.
So, you know, pi is not 3.14.
You actually want
to use a calculator
where you plug
in the number pi exactly.
So on your calculator,
you want to put 180 degrees,
and then divide by pi.
Alright. So I get
on my calculator
57.295779 approximately.
So it depends
on how far you want
to round it.
So let's say round it
to the nearest tenth
of a degree.
It would be 57.3 degrees.
So when you look
at this picture here,
this angle is approximately
57 degrees.
It's approximate.
So one radian is
about 57.3 degrees.
So note, this is the important
part, note one degree is much
smaller -
[ Pause ]
Than one radian.
So it's very important.
If you want
to write your answer
in degrees, you need to use
that degree symbol.
If you just write the number
one or you write one radian,
it means it's not in degrees.
This is your math gal,
Julie Harland.
Please visit my website
at yourmathgal dot com
where all of my videos are
organized by topic.