[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.08,0:00:01.98,Default,,0000,0000,0000,,- [Voiceover] What I want\Nto talk about in this video,
Dialogue: 0,0:00:01.98,0:00:04.79,Default,,0000,0000,0000,,is the notion of Arc Measure,
Dialogue: 0,0:00:04.79,0:00:06.95,Default,,0000,0000,0000,,when we're dealing with circles.
Dialogue: 0,0:00:06.95,0:00:09.18,Default,,0000,0000,0000,,As we'll see, sometimes when you see
Dialogue: 0,0:00:09.18,0:00:10.50,Default,,0000,0000,0000,,something like arc measure,
Dialogue: 0,0:00:10.50,0:00:12.36,Default,,0000,0000,0000,,you might think it's the length of an arc,
Dialogue: 0,0:00:12.36,0:00:14.77,Default,,0000,0000,0000,,but arc length is\Nactually a different idea.
Dialogue: 0,0:00:14.77,0:00:16.88,Default,,0000,0000,0000,,So we will compare these two things.
Dialogue: 0,0:00:16.88,0:00:20.30,Default,,0000,0000,0000,,Arc length to arc measure.
Dialogue: 0,0:00:20.30,0:00:23.27,Default,,0000,0000,0000,,So arc measure, all that is
Dialogue: 0,0:00:23.27,0:00:24.68,Default,,0000,0000,0000,,is just a fancy way of saying,
Dialogue: 0,0:00:24.68,0:00:27.08,Default,,0000,0000,0000,,if I have a circle right over here,
Dialogue: 0,0:00:27.08,0:00:29.93,Default,,0000,0000,0000,,this is my best attempt\Nat drawing a circle.
Dialogue: 0,0:00:29.93,0:00:32.56,Default,,0000,0000,0000,,I have a circle here.
Dialogue: 0,0:00:32.56,0:00:37.13,Default,,0000,0000,0000,,The center of the circle,\Nlet's call that point O,
Dialogue: 0,0:00:37.13,0:00:39.73,Default,,0000,0000,0000,,and let me put some\Nother points over here.
Dialogue: 0,0:00:39.73,0:00:43.72,Default,,0000,0000,0000,,So let's say that this is point A,
Dialogue: 0,0:00:43.72,0:00:46.84,Default,,0000,0000,0000,,let's say this is point B,
Dialogue: 0,0:00:46.84,0:00:51.18,Default,,0000,0000,0000,,and let's say this is\Npoint C right over here.
Dialogue: 0,0:00:51.18,0:00:53.22,Default,,0000,0000,0000,,And let's say that I have,
Dialogue: 0,0:00:53.22,0:00:57.05,Default,,0000,0000,0000,,let's say the central\Nangle, right over here,
Dialogue: 0,0:00:57.05,0:00:59.17,Default,,0000,0000,0000,,cause it includes the\Ncenter of the circle,
Dialogue: 0,0:00:59.17,0:01:02.11,Default,,0000,0000,0000,,so the central angle, angle AOB.
Dialogue: 0,0:01:02.11,0:01:07.08,Default,,0000,0000,0000,,Let's say it has a measure of 120 degrees.
Dialogue: 0,0:01:09.64,0:01:11.08,Default,,0000,0000,0000,,And if someone were to say,
Dialogue: 0,0:01:11.08,0:01:14.34,Default,,0000,0000,0000,,what is the measure of arc AB?
Dialogue: 0,0:01:14.77,0:01:16.32,Default,,0000,0000,0000,,So, let me write that down.
Dialogue: 0,0:01:16.32,0:01:17.60,Default,,0000,0000,0000,,The measure.
Dialogue: 0,0:01:17.60,0:01:22.48,Default,,0000,0000,0000,,So, if someone were to say\Nwhat is the measure of arc AB,
Dialogue: 0,0:01:22.48,0:01:23.92,Default,,0000,0000,0000,,and they'd write it like this,
Dialogue: 0,0:01:23.92,0:01:27.44,Default,,0000,0000,0000,,so that's referring to\Narc AB right over here.
Dialogue: 0,0:01:27.44,0:01:31.41,Default,,0000,0000,0000,,It's the minor arc, so there's\Ntwo ways to connect AB,
Dialogue: 0,0:01:31.41,0:01:33.48,Default,,0000,0000,0000,,you could connect it right over here,
Dialogue: 0,0:01:33.48,0:01:35.41,Default,,0000,0000,0000,,this is the shorter distance,
Dialogue: 0,0:01:35.41,0:01:36.94,Default,,0000,0000,0000,,or you can go the other way around,
Dialogue: 0,0:01:36.94,0:01:39.84,Default,,0000,0000,0000,,which would be what you'd\Nconsider the major arc.
Dialogue: 0,0:01:39.84,0:01:41.84,Default,,0000,0000,0000,,Now, if someone's\Nreferring to the major arc,
Dialogue: 0,0:01:41.84,0:01:44.56,Default,,0000,0000,0000,,they would say mark ACB.
Dialogue: 0,0:01:44.56,0:01:46.81,Default,,0000,0000,0000,,So when you're given just two letters,
Dialogue: 0,0:01:46.81,0:01:49.48,Default,,0000,0000,0000,,you assume it's the shortest\Ndistance between the two.
Dialogue: 0,0:01:49.48,0:01:51.66,Default,,0000,0000,0000,,You assume that it is the minor arc.
Dialogue: 0,0:01:51.66,0:01:53.47,Default,,0000,0000,0000,,In order to specify the major arc,
Dialogue: 0,0:01:53.47,0:01:55.42,Default,,0000,0000,0000,,you would give the third letter,
Dialogue: 0,0:01:55.42,0:01:57.37,Default,,0000,0000,0000,,to go the long way around.
Dialogue: 0,0:01:57.37,0:02:00.65,Default,,0000,0000,0000,,So the measure of arc AB, and sometimes
Dialogue: 0,0:02:00.65,0:02:02.64,Default,,0000,0000,0000,,you'll see it with\Nparenthesis right over here,
Dialogue: 0,0:02:02.64,0:02:05.80,Default,,0000,0000,0000,,all this is, this is the\Nsame thing as the measure
Dialogue: 0,0:02:05.80,0:02:10.18,Default,,0000,0000,0000,,of the central angle\Nthat intercepts that arc.
Dialogue: 0,0:02:10.18,0:02:12.67,Default,,0000,0000,0000,,Well, the central angle\Nthat intercepts that arc
Dialogue: 0,0:02:12.67,0:02:16.32,Default,,0000,0000,0000,,has a measure of 120 degrees.
Dialogue: 0,0:02:16.32,0:02:20.42,Default,,0000,0000,0000,,So this is just going to be 120 degrees.
Dialogue: 0,0:02:20.42,0:02:22.00,Default,,0000,0000,0000,,Now, some of y'all might be saying,
Dialogue: 0,0:02:22.00,0:02:23.51,Default,,0000,0000,0000,,well, what about the major arc?
Dialogue: 0,0:02:23.51,0:02:24.81,Default,,0000,0000,0000,,Well, let's write that.
Dialogue: 0,0:02:24.81,0:02:27.27,Default,,0000,0000,0000,,So if we're talking about arc ACB,
Dialogue: 0,0:02:27.27,0:02:29.27,Default,,0000,0000,0000,,so we're going the other way around,
Dialogue: 0,0:02:29.27,0:02:31.55,Default,,0000,0000,0000,,so this is major arc.
Dialogue: 0,0:02:31.55,0:02:36.50,Default,,0000,0000,0000,,So what is the measure of arc ACB,
Dialogue: 0,0:02:36.86,0:02:38.65,Default,,0000,0000,0000,,once again we're using three letters,
Dialogue: 0,0:02:38.65,0:02:41.07,Default,,0000,0000,0000,,so that we're specifying the major arc.
Dialogue: 0,0:02:41.07,0:02:45.13,Default,,0000,0000,0000,,Well, this angle, this\Ncentral angle right over here,
Dialogue: 0,0:02:45.13,0:02:48.87,Default,,0000,0000,0000,,to go all the way around\Nthe circle is 360 degrees.
Dialogue: 0,0:02:48.87,0:02:52.96,Default,,0000,0000,0000,,So this is going to be\Nthe 360 minus the 120
Dialogue: 0,0:02:52.96,0:02:54.63,Default,,0000,0000,0000,,that we're not including.
Dialogue: 0,0:02:54.63,0:02:57.27,Default,,0000,0000,0000,,So 360 degrees minus 120 is going to be,
Dialogue: 0,0:02:57.27,0:03:01.59,Default,,0000,0000,0000,,is going to be 240 degrees.
Dialogue: 0,0:03:01.59,0:03:06.56,Default,,0000,0000,0000,,So the measure of this angle\Nright over here is 240 degrees,
Dialogue: 0,0:03:06.97,0:03:11.80,Default,,0000,0000,0000,,so the measure of this arc,
Dialogue: 0,0:03:11.80,0:03:14.06,Default,,0000,0000,0000,,I have to be careful not\Nto say length of that arc,
Dialogue: 0,0:03:14.06,0:03:16.19,Default,,0000,0000,0000,,the measure of this arc\Nis going to be the same
Dialogue: 0,0:03:16.19,0:03:18.03,Default,,0000,0000,0000,,as the measure of the central angle.
Dialogue: 0,0:03:18.03,0:03:21.69,Default,,0000,0000,0000,,It's going to be 240 degrees.
Dialogue: 0,0:03:24.42,0:03:27.48,Default,,0000,0000,0000,,These arc measures are\Ngoing to be the case
Dialogue: 0,0:03:27.48,0:03:29.66,Default,,0000,0000,0000,,regardless of the size of the circle,
Dialogue: 0,0:03:29.66,0:03:31.38,Default,,0000,0000,0000,,and that's where the\Ndifference starts to be
Dialogue: 0,0:03:31.38,0:03:33.51,Default,,0000,0000,0000,,from arc measure to arc length.
Dialogue: 0,0:03:33.51,0:03:36.76,Default,,0000,0000,0000,,So, I could have two circles,
Dialogue: 0,0:03:36.76,0:03:38.90,Default,,0000,0000,0000,,so this circle right over here
Dialogue: 0,0:03:38.90,0:03:42.03,Default,,0000,0000,0000,,and that circle right over here,
Dialogue: 0,0:03:42.03,0:03:45.61,Default,,0000,0000,0000,,and as long as the central\Nangle that intercepts the arc
Dialogue: 0,0:03:45.61,0:03:47.88,Default,,0000,0000,0000,,has the same degree measure,
Dialogue: 0,0:03:47.88,0:03:52.88,Default,,0000,0000,0000,,so let's say that that degree\Nmeasure is the same as,
Dialogue: 0,0:03:53.02,0:03:54.36,Default,,0000,0000,0000,,these are central angles,
Dialogue: 0,0:03:54.36,0:03:55.84,Default,,0000,0000,0000,,so we're assuming the vertex of the angle
Dialogue: 0,0:03:55.84,0:03:57.28,Default,,0000,0000,0000,,is the center of the circle.
Dialogue: 0,0:03:57.28,0:03:59.56,Default,,0000,0000,0000,,As long as these two are the same,
Dialogue: 0,0:03:59.56,0:04:02.25,Default,,0000,0000,0000,,these two central angles\Nhave the same degree measure,
Dialogue: 0,0:04:02.25,0:04:05.46,Default,,0000,0000,0000,,then the arc measures, then\Nthe corresponding arc measures
Dialogue: 0,0:04:05.46,0:04:07.01,Default,,0000,0000,0000,,are going to be the same.
Dialogue: 0,0:04:07.01,0:04:10.40,Default,,0000,0000,0000,,But clearly, these two\Narc lengths are different.
Dialogue: 0,0:04:10.40,0:04:12.26,Default,,0000,0000,0000,,The arc length is not going to depend
Dialogue: 0,0:04:12.26,0:04:15.16,Default,,0000,0000,0000,,only on the measure of the central angle,
Dialogue: 0,0:04:15.16,0:04:16.97,Default,,0000,0000,0000,,the arc length is going to depend
Dialogue: 0,0:04:16.97,0:04:20.13,Default,,0000,0000,0000,,on the size of the actual circle.
Dialogue: 0,0:04:20.13,0:04:22.82,Default,,0000,0000,0000,,Arc measure is only dependent
Dialogue: 0,0:04:22.82,0:04:26.05,Default,,0000,0000,0000,,on the measure of the central angle
Dialogue: 0,0:04:26.05,0:04:28.88,Default,,0000,0000,0000,,that intercepts that arc.
Dialogue: 0,0:04:28.88,0:04:33.09,Default,,0000,0000,0000,,So your maximum arc measure\Nis going to be 360 degrees.
Dialogue: 0,0:04:33.09,0:04:36.73,Default,,0000,0000,0000,,Your minimum arc measure is\Ngoing to be zero degrees.
Dialogue: 0,0:04:36.73,0:04:39.98,Default,,0000,0000,0000,,It's measured in degrees,\Nnot in units of length
Dialogue: 0,0:04:39.98,0:04:42.56,Default,,0000,0000,0000,,that arc length would be measured in.
Dialogue: 0,0:04:42.56,0:04:44.28,Default,,0000,0000,0000,,So, let me write this down.
Dialogue: 0,0:04:44.28,0:04:46.28,Default,,0000,0000,0000,,This only depends...
Dialogue: 0,0:04:46.28,0:04:49.39,Default,,0000,0000,0000,,So, this is what's going to drive this
Dialogue: 0,0:04:49.39,0:04:54.39,Default,,0000,0000,0000,,is the measure of central\Nangle, central angle,
Dialogue: 0,0:04:57.80,0:05:00.04,Default,,0000,0000,0000,,that intercepts the arc.
Dialogue: 0,0:05:00.75,0:05:05.75,Default,,0000,0000,0000,,That intercepts, intercepts the arc.
Dialogue: 0,0:05:06.76,0:05:08.68,Default,,0000,0000,0000,,When you talk about arc length,
Dialogue: 0,0:05:08.68,0:05:10.80,Default,,0000,0000,0000,,yes, it's going to be\Ndependent on the angle,
Dialogue: 0,0:05:10.80,0:05:12.75,Default,,0000,0000,0000,,but it's also dependent,\Nit's going to be dependent
Dialogue: 0,0:05:12.75,0:05:14.23,Default,,0000,0000,0000,,on the measure of that central angle
Dialogue: 0,0:05:14.23,0:05:16.88,Default,,0000,0000,0000,,plus the size of the circle.
Dialogue: 0,0:05:16.88,0:05:19.45,Default,,0000,0000,0000,,Size of the circle.
Dialogue: 0,0:05:19.45,0:05:21.52,Default,,0000,0000,0000,,You're actually talking\Nabout a length now,
Dialogue: 0,0:05:21.52,0:05:22.94,Default,,0000,0000,0000,,when you're talking about arc length.
Dialogue: 0,0:05:22.94,0:05:25.30,Default,,0000,0000,0000,,While here, you're talking\Nabout a degree measure.