00:01
So once again, welcome to a new problem.
00:05
Whenever you think about a radiant measure, what you're saying is that if i have four quadrants and going from the x axis and this is the y axis, if i'm going all the way like this, all the way around, that's going to be 360 degrees.
00:26
If you think about this being circular, if this is the radius, and you take the radius and then laid on the, lay the radius on the surface like that, this is r.
00:44
That's going to be equivalent to one radian.
00:48
So this angle right here, data, the angle, i want to say the angle, the angle that subtends radius on the circumference is the same as one radian.
01:30
That angle is the same as one radiant.
01:33
So if the circumference is 2 pi r, then it means that how many radiance are we going to have right here? if you're going to go all the way around like this, that's a distance 2 pi r.
01:51
So how many radii or radiuses can you have around a 360? it's going to be 2 pi r, 2 pi r, 2 pi r divide by r.
02:08
So 360 degrees is equivalent to 2 pi radiance.
02:21
It's equivalent to 2 pi radiance because these two cancel out.
02:27
So now we know that if 360 is equals to 2 pi radiance, then 180 will be the same as pi radiance.
02:40
And we have a problem where we're given angles in degrees, we're given multiple angles in degrees and we're supposed to transform.
02:55
These to radiance.
02:58
So we want to transform these to radiance.
03:02
Five of them, five angles.
03:05
So determine the value of these angles in radiance.
03:21
So we'll go ahead and start with the first one where we have 30 degrees.
03:27
So 30 degrees times we want to change it to radiance.
03:31
So we'll say pi radiance is the same as 180 degrees.
03:37
So when you do that transformation, you get to see that this is, these cancel.
03:43
This is one.
03:44
This is six.
03:46
So pi over six radiance, pi over six radiance, which is approximately equals to 0 .52 radiance.
03:58
A lot of times they just leave it as pi over six radiance.
04:02
So you'll see in some cases, they just say it's pi for six.
04:07
In part b, we have 57 degrees.
04:10
We want to change that to radiance.
04:12
So we know pi radiance is 180.
04:16
And then if you divide these two into each other, for example, three goes into 57, how many times? 19 times.
04:26
And then three goes into 180, 60 times.
04:30
So this becomes the same as 19 over 60 pi radiance...