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Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:02.35,0:00:08.97,Default,,0000,0000,0000,,This video is going to look at\Nthree knew trig functions. Cosec
Dialogue: 0,0:00:08.97,0:00:10.63,Default,,0000,0000,0000,,Zack and caught.
Dialogue: 0,0:00:11.27,0:00:14.59,Default,,0000,0000,0000,,However, they're not entirely\Nknew, because they are derived
Dialogue: 0,0:00:14.59,0:00:18.65,Default,,0000,0000,0000,,from the three that we know\Nabout already sign calls and
Dialogue: 0,0:00:18.65,0:00:21.46,Default,,0000,0000,0000,,tan. So let's have a look.
Dialogue: 0,0:00:22.47,0:00:29.70,Default,,0000,0000,0000,,The first one that we want to\Nhave a look at is cosec that is
Dialogue: 0,0:00:29.70,0:00:36.45,Default,,0000,0000,0000,,defined to be one over sine. So\None over sine Theta is equal to.
Dialogue: 0,0:00:36.45,0:00:41.75,Default,,0000,0000,0000,,Now to give it its full name it\Nis the cosecant.
Dialogue: 0,0:00:41.75,0:00:49.06,Default,,0000,0000,0000,,Home theater But we\Nshorten that till cosec theater.
Dialogue: 0,0:00:49.89,0:00:57.03,Default,,0000,0000,0000,,Second one. Follows the\Nsame line one over 'cause
Dialogue: 0,0:00:57.03,0:01:04.60,Default,,0000,0000,0000,,Theater and it's full name is\Nthe secant of Theta. But again,
Dialogue: 0,0:01:04.60,0:01:12.17,Default,,0000,0000,0000,,we shorten that to set theater\Nand the final one, one over
Dialogue: 0,0:01:12.17,0:01:19.88,Default,,0000,0000,0000,,10 theater. Equals and it's\Nfull name is the cotangent of
Dialogue: 0,0:01:19.88,0:01:25.52,Default,,0000,0000,0000,,Theta, and again we shorten that\Nto caught theater.
Dialogue: 0,0:01:26.19,0:01:31.71,Default,,0000,0000,0000,,Now, why do we need these? Well,\Nfirst of all, they will help us
Dialogue: 0,0:01:31.71,0:01:34.86,Default,,0000,0000,0000,,to solve trig equations.\NSecondly, there involved in
Dialogue: 0,0:01:34.86,0:01:38.80,Default,,0000,0000,0000,,identity's and 3rd they come up\Nwhen we do calculus,
Dialogue: 0,0:01:38.80,0:01:40.37,Default,,0000,0000,0000,,particularly when we do
Dialogue: 0,0:01:40.37,0:01:45.83,Default,,0000,0000,0000,,integration. Let's just have a\Nlook at one example of where
Dialogue: 0,0:01:45.83,0:01:48.52,Default,,0000,0000,0000,,they might occur in terms of
Dialogue: 0,0:01:48.52,0:01:54.04,Default,,0000,0000,0000,,basic identity's. So the basic\Ntrig identity that we've got,
Dialogue: 0,0:01:54.04,0:01:59.80,Default,,0000,0000,0000,,the sine squared Theta Plus Cost\NSquare theater, equals 1.
Dialogue: 0,0:02:00.52,0:02:07.18,Default,,0000,0000,0000,,And if I choose to divide\Neverything on both sides of this
Dialogue: 0,0:02:07.18,0:02:12.73,Default,,0000,0000,0000,,identity by Cos squared, then\NI'll have sine squared Theta
Dialogue: 0,0:02:12.73,0:02:18.28,Default,,0000,0000,0000,,over cost Square theater plus\Ncost Square theater over Cos
Dialogue: 0,0:02:18.28,0:02:22.72,Default,,0000,0000,0000,,squared Theta equals one over\Ncost squared Theta.
Dialogue: 0,0:02:23.22,0:02:29.43,Default,,0000,0000,0000,,And so this one is sign over\Ncause all squared. So that gives
Dialogue: 0,0:02:29.43,0:02:34.69,Default,,0000,0000,0000,,us stand square theater plus\Ncost squared into Cos squared is
Dialogue: 0,0:02:34.69,0:02:40.43,Default,,0000,0000,0000,,one equals and then one over\Ncost squared is one over cause
Dialogue: 0,0:02:40.43,0:02:43.30,Default,,0000,0000,0000,,all squared. So that is set
Dialogue: 0,0:02:43.30,0:02:48.22,Default,,0000,0000,0000,,squared Theta. So there's one\Nof our new trick functions
Dialogue: 0,0:02:48.22,0:02:53.09,Default,,0000,0000,0000,,popping up in an identity this\Ntime, and there is a similar
Dialogue: 0,0:02:53.09,0:02:57.56,Default,,0000,0000,0000,,one that we can get if we\Ndivide throughout by sine
Dialogue: 0,0:02:57.56,0:03:02.83,Default,,0000,0000,0000,,squared, and if we do that, we\Nend up with one plus cot
Dialogue: 0,0:03:02.83,0:03:06.89,Default,,0000,0000,0000,,squared Theta is equal to\Ncosec squared Theta, so there
Dialogue: 0,0:03:06.89,0:03:10.55,Default,,0000,0000,0000,,the other two trig functions\Nthat we've just introduced
Dialogue: 0,0:03:10.55,0:03:11.77,Default,,0000,0000,0000,,again pop up.
Dialogue: 0,0:03:13.11,0:03:18.12,Default,,0000,0000,0000,,Let's have a look at what might\Nhappen when we reached the later
Dialogue: 0,0:03:18.12,0:03:20.04,Default,,0000,0000,0000,,stages of solving a trig
Dialogue: 0,0:03:20.04,0:03:27.28,Default,,0000,0000,0000,,equation. So let's take\Ncot squared Theta equals
Dialogue: 0,0:03:27.28,0:03:35.10,Default,,0000,0000,0000,,3 four theater between\N360 and 0 degrees.
Dialogue: 0,0:03:35.67,0:03:40.93,Default,,0000,0000,0000,,Well, we begin to solve this by\Ntaking the square root. So
Dialogue: 0,0:03:40.93,0:03:46.18,Default,,0000,0000,0000,,caught theater equals Route 3 or\Nminus Route 3. Remember, we take
Dialogue: 0,0:03:46.18,0:03:52.31,Default,,0000,0000,0000,,a square root, it has to be plus\Nor minus. Now we might think,
Dialogue: 0,0:03:52.31,0:03:58.01,Default,,0000,0000,0000,,well, let's just look this up in\Nsome tables or let's take our
Dialogue: 0,0:03:58.01,0:04:02.83,Default,,0000,0000,0000,,Calculator, but do we really\Nneed to? We know what caught
Dialogue: 0,0:04:02.83,0:04:05.45,Default,,0000,0000,0000,,theater is. It's one over Tan
Dialogue: 0,0:04:05.45,0:04:10.32,Default,,0000,0000,0000,,Theta. And that's Route 3 or\Nminus Route 3.
Dialogue: 0,0:04:10.88,0:04:16.51,Default,,0000,0000,0000,,Now we can turn this one upside\Ndown to give us Tan Theta equals
Dialogue: 0,0:04:16.51,0:04:22.14,Default,,0000,0000,0000,,and we can think of each of\Nthese as being root 3 over one
Dialogue: 0,0:04:22.14,0:04:27.76,Default,,0000,0000,0000,,or minus Route 3 over one, and\Nso we can turn these upside down
Dialogue: 0,0:04:27.76,0:04:32.59,Default,,0000,0000,0000,,to get one over Route 3 or minus\None over Route 3.
Dialogue: 0,0:04:33.47,0:04:39.57,Default,,0000,0000,0000,,And now it's in terms of Tan\NTheater and this is now one of
Dialogue: 0,0:04:39.57,0:04:44.37,Default,,0000,0000,0000,,those special values of our trig\Nfunctions. In fact, one over
Dialogue: 0,0:04:44.37,0:04:50.04,Default,,0000,0000,0000,,Route 3 is the tangent of 30\Ndegrees, so we know that this
Dialogue: 0,0:04:50.04,0:04:54.83,Default,,0000,0000,0000,,has one solution that is 30\Ndegrees. But what about the
Dialogue: 0,0:04:54.83,0:04:58.76,Default,,0000,0000,0000,,other solutions? Well, let's\Nhave a look at those.
Dialogue: 0,0:05:00.08,0:05:01.70,Default,,0000,0000,0000,,Sketch of the graph.
Dialogue: 0,0:05:02.39,0:05:10.00,Default,,0000,0000,0000,,Tan Theta 0 up to\N90 from 90 up through
Dialogue: 0,0:05:10.00,0:05:13.04,Default,,0000,0000,0000,,180 up towards 270.
Dialogue: 0,0:05:13.85,0:05:17.03,Default,,0000,0000,0000,,Stopping there at\N360, so that's not.
Dialogue: 0,0:05:18.27,0:05:22.03,Default,,0000,0000,0000,,9180, two, 70
Dialogue: 0,0:05:22.03,0:05:28.45,Default,,0000,0000,0000,,and 360. And\Nthe tangent of 30 is one over
Dialogue: 0,0:05:28.45,0:05:33.56,Default,,0000,0000,0000,,Route 3. So somewhere here is\None over Route 3 coming down to
Dialogue: 0,0:05:33.56,0:05:38.67,Default,,0000,0000,0000,,30. So of course the next one is\Nacross there and the symmetry
Dialogue: 0,0:05:38.67,0:05:44.96,Default,,0000,0000,0000,,tells us if this is 30 on from\Nzero. This is 30 on from 180, so
Dialogue: 0,0:05:44.96,0:05:49.68,Default,,0000,0000,0000,,the next one is 210 degrees\Nminus one over Route 3. Well,
Dialogue: 0,0:05:49.68,0:05:51.64,Default,,0000,0000,0000,,that's going to be somewhere
Dialogue: 0,0:05:51.64,0:05:56.80,Default,,0000,0000,0000,,along here. And again, the\Nsymmetry tells us if this is 30
Dialogue: 0,0:05:56.80,0:06:02.48,Default,,0000,0000,0000,,on this way, then this one is 30\Nback this way. So that gives us
Dialogue: 0,0:06:02.48,0:06:06.28,Default,,0000,0000,0000,,150 degrees and we've got\Nanother value here which is
Dialogue: 0,0:06:06.28,0:06:11.20,Default,,0000,0000,0000,,going to be 30 back from there,\Nwhich is going to be 330
Dialogue: 0,0:06:11.20,0:06:15.65,Default,,0000,0000,0000,,degrees. So solving equations\Nthat involve things like caught,
Dialogue: 0,0:06:15.65,0:06:20.91,Default,,0000,0000,0000,,encek and Cosec is no different\Nto solving equations to do with
Dialogue: 0,0:06:20.91,0:06:26.17,Default,,0000,0000,0000,,sign causing tan because we just\Nturn them into sign calls and
Dialogue: 0,0:06:26.17,0:06:31.86,Default,,0000,0000,0000,,tab to conclude this, we're just\Ngoing to have a look at the
Dialogue: 0,0:06:31.86,0:06:34.49,Default,,0000,0000,0000,,graphs of these three knew trig
Dialogue: 0,0:06:34.49,0:06:40.43,Default,,0000,0000,0000,,functions. And in order to do\Nthat, we will begin each one by
Dialogue: 0,0:06:40.43,0:06:44.66,Default,,0000,0000,0000,,looking at the graph of the\Nrelated trig function. So to
Dialogue: 0,0:06:44.66,0:06:49.67,Default,,0000,0000,0000,,look at Cosec, we're going to\Nlook at sign first. So what does
Dialogue: 0,0:06:49.67,0:06:51.21,Default,,0000,0000,0000,,the graph of sign?
Dialogue: 0,0:06:52.48,0:06:58.87,Default,,0000,0000,0000,,Look like. Will take one\Ncomplete cycle between North and
Dialogue: 0,0:06:58.87,0:07:01.60,Default,,0000,0000,0000,,360. So 0.
Dialogue: 0,0:07:02.46,0:07:09.16,Default,,0000,0000,0000,,180, three, 160 and the\Npeak and trough are in
Dialogue: 0,0:07:09.16,0:07:15.86,Default,,0000,0000,0000,,between 1970 and that goes\Nfrom one down 2 -
Dialogue: 0,0:07:15.86,0:07:22.56,Default,,0000,0000,0000,,1 and what we're going\Nto graph now is cosec
Dialogue: 0,0:07:22.56,0:07:29.26,Default,,0000,0000,0000,,theater, which of course is\None over sine Theta. So
Dialogue: 0,0:07:29.26,0:07:32.61,Default,,0000,0000,0000,,let's set up similar axes.
Dialogue: 0,0:07:32.74,0:07:36.02,Default,,0000,0000,0000,,So mark them off, there's 90.
Dialogue: 0,0:07:36.55,0:07:39.31,Default,,0000,0000,0000,,180 270
Dialogue: 0,0:07:39.96,0:07:46.63,Default,,0000,0000,0000,,360 Now\Nhere at 90
Dialogue: 0,0:07:46.63,0:07:53.77,Default,,0000,0000,0000,,the value of\Nsign is warm.
Dialogue: 0,0:07:54.84,0:08:02.16,Default,,0000,0000,0000,,So at 90 the value of cosec must\Nalso be one, so I'm going to
Dialogue: 0,0:08:02.16,0:08:08.50,Default,,0000,0000,0000,,market their one here at 270.\NThe value of sign is minus one.
Dialogue: 0,0:08:09.07,0:08:14.45,Default,,0000,0000,0000,,And so at 270, the value of\Ncosec must be one over minus
Dialogue: 0,0:08:14.45,0:08:16.94,Default,,0000,0000,0000,,one, which again is just minus
Dialogue: 0,0:08:16.94,0:08:19.80,Default,,0000,0000,0000,,one. So there are two points.
Dialogue: 0,0:08:20.42,0:08:22.94,Default,,0000,0000,0000,,What about this point?
Dialogue: 0,0:08:23.57,0:08:29.21,Default,,0000,0000,0000,,Here at zero the sign of\N0 is 0.
Dialogue: 0,0:08:30.11,0:08:34.28,Default,,0000,0000,0000,,So the value of Cosec would be\None over 0.
Dialogue: 0,0:08:35.35,0:08:40.22,Default,,0000,0000,0000,,But we're not allowed to divide\Nby zero, but we can divide by
Dialogue: 0,0:08:40.22,0:08:45.10,Default,,0000,0000,0000,,something a little bit away.\NWhat we can see is that would be
Dialogue: 0,0:08:45.10,0:08:49.98,Default,,0000,0000,0000,,a very very tiny positive number\Nthat we were dividing by. So if
Dialogue: 0,0:08:49.98,0:08:54.48,Default,,0000,0000,0000,,we divide 1 by a very tiny\Npositive number, the answer has
Dialogue: 0,0:08:54.48,0:08:59.35,Default,,0000,0000,0000,,to be very big, but still\Npositive. So with a bit of curve
Dialogue: 0,0:08:59.35,0:09:01.98,Default,,0000,0000,0000,,there, let's have a look at 180.
Dialogue: 0,0:09:02.65,0:09:09.80,Default,,0000,0000,0000,,Well, at 180 sign of Theta is\Nagain 0 so cosec is one over
Dialogue: 0,0:09:09.80,0:09:16.96,Default,,0000,0000,0000,,0 at this 180 degrees. Let's go\Na little bit this side here of
Dialogue: 0,0:09:16.96,0:09:23.09,Default,,0000,0000,0000,,180 and the value of sign is\Nreally very small. It's very
Dialogue: 0,0:09:23.09,0:09:24.62,Default,,0000,0000,0000,,close to 0.
Dialogue: 0,0:09:25.13,0:09:31.74,Default,,0000,0000,0000,,So again, 1 divided by something\Nvery small and positive.
Dialogue: 0,0:09:32.24,0:09:37.84,Default,,0000,0000,0000,,Is again something very large\Nand positive, so let me put in
Dialogue: 0,0:09:37.84,0:09:41.63,Default,,0000,0000,0000,,an asymptotes. And we've got a\Npiece of curve there.
Dialogue: 0,0:09:42.16,0:09:47.02,Default,,0000,0000,0000,,Now this curve goes like that.\NWhat we're seeing is that this
Dialogue: 0,0:09:47.02,0:09:52.69,Default,,0000,0000,0000,,curve is going to come down and\Nup like that, and it's going to
Dialogue: 0,0:09:52.69,0:09:57.14,Default,,0000,0000,0000,,do the same here, except because\Nwhat we're dividing by are
Dialogue: 0,0:09:57.14,0:09:59.17,Default,,0000,0000,0000,,negative numbers, it's going to
Dialogue: 0,0:09:59.17,0:10:01.12,Default,,0000,0000,0000,,be like. That
Dialogue: 0,0:10:02.03,0:10:08.40,Default,,0000,0000,0000,,So there's our graph of cosec\Nderived from the graph of sign.
Dialogue: 0,0:10:10.91,0:10:14.81,Default,,0000,0000,0000,,Let's take now calls feta.
Dialogue: 0,0:10:15.34,0:10:16.71,Default,,0000,0000,0000,,Do the same.
Dialogue: 0,0:10:17.94,0:10:25.64,Default,,0000,0000,0000,,Will take the graph of\Ncostita between North and 360.
Dialogue: 0,0:10:25.64,0:10:33.18,Default,,0000,0000,0000,,At the extreme, values will\Nbe minus one plus one
Dialogue: 0,0:10:33.18,0:10:36.95,Default,,0000,0000,0000,,9180 two 7360. Just make
Dialogue: 0,0:10:36.95,0:10:41.87,Default,,0000,0000,0000,,that clearer. And so let's have\Na look here.
Dialogue: 0,0:10:42.98,0:10:46.67,Default,,0000,0000,0000,,Mark off the same
Dialogue: 0,0:10:46.67,0:10:53.56,Default,,0000,0000,0000,,points. And we're\Ngraphing SEK this
Dialogue: 0,0:10:53.56,0:11:00.74,Default,,0000,0000,0000,,time sex theater,\Nwhich is one
Dialogue: 0,0:11:00.74,0:11:04.32,Default,,0000,0000,0000,,over 'cause theater.
Dialogue: 0,0:11:05.00,0:11:07.40,Default,,0000,0000,0000,,So again, let's Mark some
Dialogue: 0,0:11:07.40,0:11:10.94,Default,,0000,0000,0000,,points. Here when theater is 0.
Dialogue: 0,0:11:11.65,0:11:16.42,Default,,0000,0000,0000,,Costita is one Soucek\NTheater is one over one
Dialogue: 0,0:11:16.42,0:11:22.78,Default,,0000,0000,0000,,which is one. So will mark\Nthe one there here at 180.
Dialogue: 0,0:11:24.01,0:11:29.08,Default,,0000,0000,0000,,Cost theater is minus one.\NSoucek Theater is 1 divided
Dialogue: 0,0:11:29.08,0:11:34.15,Default,,0000,0000,0000,,by minus one and so will\Nmark minus one here.
Dialogue: 0,0:11:35.49,0:11:40.14,Default,,0000,0000,0000,,Here at 90 we got exactly the\Nsame problems we have before the
Dialogue: 0,0:11:40.14,0:11:45.87,Default,,0000,0000,0000,,value of Cos theater at 90 zero.\NSo 1 / 0 is a very big number.
Dialogue: 0,0:11:45.87,0:11:51.24,Default,,0000,0000,0000,,Well, in fact we're not allowed\Nto do it, so we have to go a
Dialogue: 0,0:11:51.24,0:11:56.61,Default,,0000,0000,0000,,little bit away from 90 to get a\Nvalue of Cos Theta which is very
Dialogue: 0,0:11:56.61,0:12:01.62,Default,,0000,0000,0000,,small, close to 0 but positive.\NAnd if we divide 1 by that small
Dialogue: 0,0:12:01.62,0:12:05.56,Default,,0000,0000,0000,,positive number, the answer that\Nwe get is very big and.
Dialogue: 0,0:12:05.64,0:12:10.40,Default,,0000,0000,0000,,Positive so we have a bit of\Ncurve going up like that. What
Dialogue: 0,0:12:10.40,0:12:15.16,Default,,0000,0000,0000,,about this side of 90? Well this\Nside of 90 where dividing by
Dialogue: 0,0:12:15.16,0:12:19.18,Default,,0000,0000,0000,,something which the value of Cos\NTheta is very small but
Dialogue: 0,0:12:19.18,0:12:23.21,Default,,0000,0000,0000,,definitely negative. So the\Nanswer is going to be very big
Dialogue: 0,0:12:23.21,0:12:28.33,Default,,0000,0000,0000,,in size when we divide it into\None but negative. So a bit of
Dialogue: 0,0:12:28.33,0:12:32.72,Default,,0000,0000,0000,,the curve here coming down to\Ntheir same problem again at 270
Dialogue: 0,0:12:32.72,0:12:36.75,Default,,0000,0000,0000,,so we can see the curve is going\Nto go round.
Dialogue: 0,0:12:36.76,0:12:40.71,Default,,0000,0000,0000,,And back like that. And then\Nhere again at 360, we're going
Dialogue: 0,0:12:40.71,0:12:44.98,Default,,0000,0000,0000,,to be able to mark that point.\NWe're going to have that one
Dialogue: 0,0:12:44.98,0:12:46.30,Default,,0000,0000,0000,,coming down at that.
Dialogue: 0,0:12:46.99,0:12:50.22,Default,,0000,0000,0000,,So there we've managed to get\Nthe graph of SEK.
Dialogue: 0,0:12:51.04,0:12:54.71,Default,,0000,0000,0000,,Out of the graph, of course.
Dialogue: 0,0:12:54.71,0:13:00.58,Default,,0000,0000,0000,,Let's now have a look at the\Ngraph of Tan Theater.
Dialogue: 0,0:13:02.28,0:13:09.53,Default,,0000,0000,0000,,These\Noff
Dialogue: 0,0:13:09.53,0:13:16.78,Default,,0000,0000,0000,,9180,\Ntwo,
Dialogue: 0,0:13:16.78,0:13:24.02,Default,,0000,0000,0000,,70\Nand
Dialogue: 0,0:13:24.02,0:13:32.26,Default,,0000,0000,0000,,360.\NAnd now we'll have a look at
Dialogue: 0,0:13:32.26,0:13:36.66,Default,,0000,0000,0000,,caught theater, which is one\Nover Tan Theater.
Dialogue: 0,0:13:37.39,0:13:43.58,Default,,0000,0000,0000,,So we'll take the same graph and\NI'll do the same as I've done
Dialogue: 0,0:13:43.58,0:13:45.35,Default,,0000,0000,0000,,before. Mark these off.
Dialogue: 0,0:13:45.86,0:13:49.70,Default,,0000,0000,0000,,So we're using the same
Dialogue: 0,0:13:49.70,0:13:55.61,Default,,0000,0000,0000,,scale. OK, let's have a look\Nwhat's happening here. This bit
Dialogue: 0,0:13:55.61,0:14:00.71,Default,,0000,0000,0000,,of curve between North and 90.\NWe begin with something for tan
Dialogue: 0,0:14:00.71,0:14:03.26,Default,,0000,0000,0000,,that is very small but positive.
Dialogue: 0,0:14:03.96,0:14:09.06,Default,,0000,0000,0000,,Just above 0 and then it gets\Nbigger and bigger and bigger as
Dialogue: 0,0:14:09.06,0:14:12.98,Default,,0000,0000,0000,,it rises. The value of Tan Theta\Nrises towards Infinity.
Dialogue: 0,0:14:14.15,0:14:19.10,Default,,0000,0000,0000,,Well down here divide the value\Nof theater is very near to zero
Dialogue: 0,0:14:19.10,0:14:24.06,Default,,0000,0000,0000,,and so tan Theta is very small\Nbut positive. So when we divide
Dialogue: 0,0:14:24.06,0:14:28.25,Default,,0000,0000,0000,,into one we're going to get\Nsomething very big and positive
Dialogue: 0,0:14:28.25,0:14:30.15,Default,,0000,0000,0000,,self. But if curve there.
Dialogue: 0,0:14:30.78,0:14:34.93,Default,,0000,0000,0000,,Up here, the value of Tan\NTheater is enormous. It's huge.
Dialogue: 0,0:14:34.93,0:14:39.83,Default,,0000,0000,0000,,So if we divide something huge\Ninto one, the answer is going to
Dialogue: 0,0:14:39.83,0:14:44.73,Default,,0000,0000,0000,,be very nearly zero. And the\Ncloser we get to 90, the closer
Dialogue: 0,0:14:44.73,0:14:46.61,Default,,0000,0000,0000,,it would be to 0.
Dialogue: 0,0:14:47.47,0:14:51.75,Default,,0000,0000,0000,,So now if we look here, we can\Nsee we've got something very,
Dialogue: 0,0:14:51.75,0:14:56.02,Default,,0000,0000,0000,,very big, but negative. So the\Nanswer is going to be very, very
Dialogue: 0,0:14:56.02,0:14:59.97,Default,,0000,0000,0000,,small, but also negative. This\Nis going to be coming out of
Dialogue: 0,0:14:59.97,0:15:02.96,Default,,0000,0000,0000,,that point there. Here 180.
Dialogue: 0,0:15:03.51,0:15:08.27,Default,,0000,0000,0000,,Got a problem at 180. Tan\NTheater is 0 one over 10 theater
Dialogue: 0,0:15:08.27,0:15:13.39,Default,,0000,0000,0000,,is there for something very very\Nbig so we can put in an acid
Dialogue: 0,0:15:13.39,0:15:18.15,Default,,0000,0000,0000,,tote and we can see we've got\Nexactly the same problem here at
Dialogue: 0,0:15:18.15,0:15:23.86,Default,,0000,0000,0000,,360. So if I join up what I've\Ngot in the direction of what's
Dialogue: 0,0:15:23.86,0:15:27.68,Default,,0000,0000,0000,,happening, we're getting a very\Nsimilar curve and repeat it over
Dialogue: 0,0:15:27.68,0:15:31.15,Default,,0000,0000,0000,,here, 'cause the curves are\Nrepeated. We're getting a very
Dialogue: 0,0:15:31.15,0:15:32.88,Default,,0000,0000,0000,,similar curve, except the other
Dialogue: 0,0:15:32.88,0:15:38.75,Default,,0000,0000,0000,,way around. So we've seen again\Nhow we can derive the graph of
Dialogue: 0,0:15:38.75,0:15:42.14,Default,,0000,0000,0000,,coffee to directly from the\Ngraph of Tan.
Dialogue: 0,0:15:42.74,0:15:45.100,Default,,0000,0000,0000,,So remember these three\Nnew functions.
Dialogue: 0,0:15:47.22,0:15:50.36,Default,,0000,0000,0000,,Co sack sack and caught.
Dialogue: 0,0:15:51.70,0:15:56.02,Default,,0000,0000,0000,,Respectively, they are one\Nover sign, one over cosine
Dialogue: 0,0:15:56.02,0:15:57.94,Default,,0000,0000,0000,,and one over Tangent.
Dialogue: 0,0:15:59.04,0:16:00.96,Default,,0000,0000,0000,,We can use them to solve
Dialogue: 0,0:16:00.96,0:16:05.52,Default,,0000,0000,0000,,equations. But each time we\Ncan get back to using sign
Dialogue: 0,0:16:05.52,0:16:08.73,Default,,0000,0000,0000,,cause and tab to help us\Nworkout the angles.