[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.86,0:00:04.48,Default,,0000,0000,0000,,Let's just do a ton of more examples, just so we\Nmake sure that we're getting
Dialogue: 0,0:00:04.48,0:00:07.02,Default,,0000,0000,0000,,this trig function thing down well.
Dialogue: 0,0:00:07.02,0:00:11.11,Default,,0000,0000,0000,,So let's construct ourselves some right triangles.
Dialogue: 0,0:00:11.11,0:00:15.30,Default,,0000,0000,0000,,Let's construct ourselves some right triangles, and I want to be very clear the way I've defined
Dialogue: 0,0:00:15.30,0:00:19.83,Default,,0000,0000,0000,,it so far, this will only work in right triangles,\Nso if you're trying to find
Dialogue: 0,0:00:19.83,0:00:24.20,Default,,0000,0000,0000,,the trig functions of angles that aren't part of right triangles, we're going to see that we're going to
Dialogue: 0,0:00:24.20,0:00:28.08,Default,,0000,0000,0000,,have to construct right triangles, but let's just focus on the right triangles for now.
Dialogue: 0,0:00:28.08,0:00:33.47,Default,,0000,0000,0000,,So let's say that I have a triangle, where\Nlet's say this length down here is seven,
Dialogue: 0,0:00:33.47,0:00:39.19,Default,,0000,0000,0000,,and let's say the length of this side up here, let's say that that is four.
Dialogue: 0,0:00:39.19,0:00:43.17,Default,,0000,0000,0000,,Let's figure out what the hypotenuse over here is going to be. So we know
Dialogue: 0,0:00:43.17,0:00:45.35,Default,,0000,0000,0000,,-let's call the hypotenuse "h"-
Dialogue: 0,0:00:45.35,0:00:52.75,Default,,0000,0000,0000,,we know that h squared is going to be equal\Nto seven squared plus four squared, we know
Dialogue: 0,0:00:52.75,0:00:55.11,Default,,0000,0000,0000,,that from of the Pythagorean theorem,
Dialogue: 0,0:00:55.11,0:00:57.19,Default,,0000,0000,0000,,that the hypotenuse squared is equal to
Dialogue: 0,0:00:57.19,0:01:00.29,Default,,0000,0000,0000,,the square of each of the sum of the squares
Dialogue: 0,0:01:00.29,0:01:04.37,Default,,0000,0000,0000,,of the other two sides. Eight squared is equal to seven\Nsquared plus four squared.
Dialogue: 0,0:01:04.37,0:01:08.15,Default,,0000,0000,0000,,So this is equal to forty-nine
Dialogue: 0,0:01:08.15,0:01:09.73,Default,,0000,0000,0000,,plus sixteen,
Dialogue: 0,0:01:09.73,0:01:11.74,Default,,0000,0000,0000,,forty-nine plus sixteen,
Dialogue: 0,0:01:11.74,0:01:16.85,Default,,0000,0000,0000,,forty nine plus ten is fifty-nine, plus\Nsix is
Dialogue: 0,0:01:16.85,0:01:21.98,Default,,0000,0000,0000,,sixty-five. It is sixty five so this h squared,
Dialogue: 0,0:01:21.98,0:01:23.91,Default,,0000,0000,0000,,let me write: h squared
Dialogue: 0,0:01:23.91,0:01:28.31,Default,,0000,0000,0000,,-that's different shade of yellow- so we have h squared is equal to
Dialogue: 0,0:01:28.31,0:01:32.48,Default,,0000,0000,0000,,sixty-five. Did I do that right? Forty nine plus ten is fifty nine, plus another six
Dialogue: 0,0:01:32.48,0:01:36.65,Default,,0000,0000,0000,,is sixty-five, or we could say that h is equal to, if we take the square root of
Dialogue: 0,0:01:36.65,0:01:38.12,Default,,0000,0000,0000,,both sides
Dialogue: 0,0:01:38.12,0:01:39.34,Default,,0000,0000,0000,,square root
Dialogue: 0,0:01:39.34,0:01:42.85,Default,,0000,0000,0000,,square root of sixty five. And we really can't simplify\Nthis at all
Dialogue: 0,0:01:42.85,0:01:44.35,Default,,0000,0000,0000,,this is thirteen
Dialogue: 0,0:01:44.35,0:01:48.82,Default,,0000,0000,0000,,this is the same thing as thirteen times five,\Nboth of those are not perfect squares and
Dialogue: 0,0:01:48.82,0:01:51.86,Default,,0000,0000,0000,,they're both prime so you can't simplify this any more.
Dialogue: 0,0:01:51.86,0:01:54.67,Default,,0000,0000,0000,,So this is equal to the square root
Dialogue: 0,0:01:54.67,0:01:56.25,Default,,0000,0000,0000,,of sixty five.
Dialogue: 0,0:01:56.25,0:02:04.96,Default,,0000,0000,0000,,Now let's find the trig, let's find the trig functions for this angle\Nup here. Let's call that angle up there theta.
Dialogue: 0,0:02:05.06,0:02:06.27,Default,,0000,0000,0000,,So whenever you do it
Dialogue: 0,0:02:06.27,0:02:09.68,Default,,0000,0000,0000,,you always want to write down - at least for\Nme it works out to write down -
Dialogue: 0,0:02:09.68,0:02:11.22,Default,,0000,0000,0000,,"soh cah toa".
Dialogue: 0,0:02:11.22,0:02:12.83,Default,,0000,0000,0000,,soh...
Dialogue: 0,0:02:12.83,0:02:16.43,Default,,0000,0000,0000,,...soh cah toa. I have these vague memories
Dialogue: 0,0:02:16.43,0:02:17.92,Default,,0000,0000,0000,,of my
Dialogue: 0,0:02:17.92,0:02:21.03,Default,,0000,0000,0000,,trigonometry teacher, maybe I've read it in some\Nbook, I don't know - you know, some, about
Dialogue: 0,0:02:21.03,0:02:25.16,Default,,0000,0000,0000,,some type of indian princess named "soh cah toa" or whatever, but it's a very useful
Dialogue: 0,0:02:25.16,0:02:28.08,Default,,0000,0000,0000,,pneumonic, so we can apply "soh cah toa". Let's find
Dialogue: 0,0:02:28.08,0:02:34.10,Default,,0000,0000,0000,,let's say we want to find the cosine. We want to find the cosine of our angle.
Dialogue: 0,0:02:34.10,0:02:37.78,Default,,0000,0000,0000,,we wanna find the cosine of our angle, you\Nsay: "soh cah toa!"
Dialogue: 0,0:02:37.78,0:02:41.22,Default,,0000,0000,0000,,So the "cah". "Cah" tells us what to do with cosine,
Dialogue: 0,0:02:41.22,0:02:43.07,Default,,0000,0000,0000,,the "cah" part tells us
Dialogue: 0,0:02:43.07,0:02:46.93,Default,,0000,0000,0000,,that cosine is adjacent over hypotenuse.
Dialogue: 0,0:02:46.93,0:02:49.98,Default,,0000,0000,0000,,Cosine is equal to adjacent
Dialogue: 0,0:02:49.98,0:02:51.53,Default,,0000,0000,0000,,over hypotenuse.
Dialogue: 0,0:02:51.53,0:02:55.91,Default,,0000,0000,0000,,So let's look over here to theta; what side is adjacent?
Dialogue: 0,0:02:55.91,0:02:57.76,Default,,0000,0000,0000,,Well we know that the hypotenuse
Dialogue: 0,0:02:57.76,0:03:00.64,Default,,0000,0000,0000,,we know that that hypotenuse is this side over here
Dialogue: 0,0:03:00.64,0:03:04.58,Default,,0000,0000,0000,,so it can't be that side. The only other side that's kind of adjacent to it that
Dialogue: 0,0:03:04.58,0:03:06.95,Default,,0000,0000,0000,,isn't the hypotenuse, is this four.
Dialogue: 0,0:03:06.95,0:03:10.48,Default,,0000,0000,0000,,So the adjacent side over here, that side is,
Dialogue: 0,0:03:10.48,0:03:14.15,Default,,0000,0000,0000,,it's literally right next to the angle, it's one of\Nthe sides that kind of forms the angle
Dialogue: 0,0:03:14.15,0:03:15.27,Default,,0000,0000,0000,,it's four
Dialogue: 0,0:03:15.27,0:03:16.67,Default,,0000,0000,0000,,over the hypotenuse.
Dialogue: 0,0:03:16.67,0:03:21.93,Default,,0000,0000,0000,,The hypotenuse we already know is square root\Nof sixty-five, so it's four
Dialogue: 0,0:03:21.93,0:03:22.47,Default,,0000,0000,0000,,over
Dialogue: 0,0:03:22.47,0:03:25.13,Default,,0000,0000,0000,,the square root of sixty-five.
Dialogue: 0,0:03:25.13,0:03:29.46,Default,,0000,0000,0000,,And sometimes people will want you to rationalize\Nthe denominator which means they don't like
Dialogue: 0,0:03:29.46,0:03:34.05,Default,,0000,0000,0000,,to have an irrational number in the denominator,\Nlike the square root of sixty five
Dialogue: 0,0:03:34.05,0:03:37.56,Default,,0000,0000,0000,,and if they - if you wanna rewrite this without\Na
Dialogue: 0,0:03:37.56,0:03:41.18,Default,,0000,0000,0000,,irrational number in the denominator, you can\Nmultiply the numerator and the denominator
Dialogue: 0,0:03:41.18,0:03:43.05,Default,,0000,0000,0000,,by the square root of sixty-five.
Dialogue: 0,0:03:43.05,0:03:47.41,Default,,0000,0000,0000,,This clearly will not change the number, because we're multiplying it by something over itself, so we're
Dialogue: 0,0:03:47.41,0:03:51.28,Default,,0000,0000,0000,,multiplying the number by one. That won't change\Nthe number, but at least it gets rid of the
Dialogue: 0,0:03:51.28,0:03:54.54,Default,,0000,0000,0000,,irrational number in the denominator. So the numerator\Nbecomes
Dialogue: 0,0:03:54.54,0:03:57.75,Default,,0000,0000,0000,,four times the square root of sixty-five,
Dialogue: 0,0:03:57.75,0:04:03.28,Default,,0000,0000,0000,,and the denominator, square root of sixty five times\Nsquare root of sixty-five, is just going to be sixty-five.
Dialogue: 0,0:04:03.28,0:04:07.13,Default,,0000,0000,0000,,We didn't get rid of the irrational number, it's still\Nthere, but it's now in the numerator.
Dialogue: 0,0:04:07.13,0:04:09.63,Default,,0000,0000,0000,,Now let's do the other trig functions
Dialogue: 0,0:04:09.63,0:04:13.22,Default,,0000,0000,0000,,or at least the other core trig functions. We'll\Nlearn in the future that there's a ton of them
Dialogue: 0,0:04:13.22,0:04:15.25,Default,,0000,0000,0000,,but they're all derived from these
Dialogue: 0,0:04:15.25,0:04:19.89,Default,,0000,0000,0000,,so let's think about what the sign of theta is. Once again\Ngo to "soh cah toa"
Dialogue: 0,0:04:19.89,0:04:25.65,Default,,0000,0000,0000,,the "soh" tells what to do with sine. Sine is opposite over hypotenuse.
Dialogue: 0,0:04:25.65,0:04:27.38,Default,,0000,0000,0000,,Sine is equal to
Dialogue: 0,0:04:27.38,0:04:31.51,Default,,0000,0000,0000,,opposite over hypotenuse. Sine is opposite over hypotenuse.
Dialogue: 0,0:04:31.51,0:04:34.02,Default,,0000,0000,0000,,So for this angle what side is opposite?
Dialogue: 0,0:04:34.02,0:04:38.93,Default,,0000,0000,0000,,We just go opposite it, what it opens into, it's opposite\Nthe seven
Dialogue: 0,0:04:38.93,0:04:41.91,Default,,0000,0000,0000,,so the opposite side is the seven.
Dialogue: 0,0:04:41.91,0:04:44.35,Default,,0000,0000,0000,,This right here - that is the opposite side
Dialogue: 0,0:04:44.35,0:04:45.71,Default,,0000,0000,0000,,and then in the
Dialogue: 0,0:04:45.71,0:04:50.01,Default,,0000,0000,0000,,hypotenuse, it's opposite over hypotenuse. the hypotenuse is the
Dialogue: 0,0:04:50.01,0:04:52.76,Default,,0000,0000,0000,,square root of sixty-five
Dialogue: 0,0:04:52.76,0:04:57.99,Default,,0000,0000,0000,,and once again if we wanted to rationalize this,\Nwe could multiply times the square root of sixty-five
Dialogue: 0,0:04:57.99,0:05:00.47,Default,,0000,0000,0000,,over the square root of sixty-five
Dialogue: 0,0:05:00.47,0:05:06.50,Default,,0000,0000,0000,,and the the numerator, we'll get seven square root of sixty-five\Nand in the denominator we will get just
Dialogue: 0,0:05:06.50,0:05:08.09,Default,,0000,0000,0000,,sixty-five again.
Dialogue: 0,0:05:08.09,0:05:10.22,Default,,0000,0000,0000,,Now let's do tangent!
Dialogue: 0,0:05:10.22,0:05:12.48,Default,,0000,0000,0000,,Let us do tangent.
Dialogue: 0,0:05:12.48,0:05:15.55,Default,,0000,0000,0000,,So if i ask you the tangent
Dialogue: 0,0:05:15.55,0:05:17.33,Default,,0000,0000,0000,,of - the tangent of theta
Dialogue: 0,0:05:17.33,0:05:19.98,Default,,0000,0000,0000,,once again go back to soh cah
Dialogue: 0,0:05:19.98,0:05:23.12,Default,,0000,0000,0000,,toa the toa part tells us what to do a tangent
Dialogue: 0,0:05:23.12,0:05:24.55,Default,,0000,0000,0000,,it tells us
Dialogue: 0,0:05:24.55,0:05:27.32,Default,,0000,0000,0000,,it tells us that tangent
Dialogue: 0,0:05:27.32,0:05:31.99,Default,,0000,0000,0000,,is equal to opposite over adjacent is equal\Nto opposite
Dialogue: 0,0:05:31.99,0:05:33.38,Default,,0000,0000,0000,,over
Dialogue: 0,0:05:33.38,0:05:35.64,Default,,0000,0000,0000,,opposite over adjacent
Dialogue: 0,0:05:35.64,0:05:36.97,Default,,0000,0000,0000,,so for this angle
Dialogue: 0,0:05:36.97,0:05:41.38,Default,,0000,0000,0000,,what is opposite we've already figured it\Nout it's seven it opens into the seventh opposite
Dialogue: 0,0:05:41.38,0:05:42.55,Default,,0000,0000,0000,,the seven
Dialogue: 0,0:05:42.55,0:05:44.41,Default,,0000,0000,0000,,so it's seven
Dialogue: 0,0:05:44.41,0:05:46.09,Default,,0000,0000,0000,,over what side is adjacent
Dialogue: 0,0:05:46.09,0:05:48.01,Default,,0000,0000,0000,,well this four is adjacent
Dialogue: 0,0:05:48.01,0:05:51.04,Default,,0000,0000,0000,,this four is adjacent so the adjacent side is\Nfour
Dialogue: 0,0:05:51.04,0:05:52.64,Default,,0000,0000,0000,,so it's seven
Dialogue: 0,0:05:52.64,0:05:54.05,Default,,0000,0000,0000,,over four
Dialogue: 0,0:05:54.05,0:05:54.95,Default,,0000,0000,0000,,and we're done
Dialogue: 0,0:05:54.95,0:05:59.35,Default,,0000,0000,0000,,we figured out all of the trig ratios for\Ntheta let's do another one
Dialogue: 0,0:05:59.35,0:06:03.13,Default,,0000,0000,0000,,let's do another one. i'll make it a little bit concrete\N'cause right now we've been saying oh was
Dialogue: 0,0:06:03.13,0:06:06.88,Default,,0000,0000,0000,,tangent of x, tangent of theta. let's make it a little bit more concrete
Dialogue: 0,0:06:06.88,0:06:08.31,Default,,0000,0000,0000,,let's say
Dialogue: 0,0:06:08.31,0:06:11.06,Default,,0000,0000,0000,,let's say, let me draw another right triangle
Dialogue: 0,0:06:11.06,0:06:13.100,Default,,0000,0000,0000,,that's another right triangle here
Dialogue: 0,0:06:13.100,0:06:15.25,Default,,0000,0000,0000,,everything we're dealing with
Dialogue: 0,0:06:15.25,0:06:18.11,Default,,0000,0000,0000,,these are going to be right triangles
Dialogue: 0,0:06:18.11,0:06:19.65,Default,,0000,0000,0000,,let's say the hypotenuse
Dialogue: 0,0:06:19.65,0:06:21.92,Default,,0000,0000,0000,,has length four
Dialogue: 0,0:06:21.92,0:06:24.44,Default,,0000,0000,0000,,let's say that this side over here
Dialogue: 0,0:06:24.44,0:06:26.47,Default,,0000,0000,0000,,has length two
Dialogue: 0,0:06:26.47,0:06:31.83,Default,,0000,0000,0000,,and let's say that this length over here is goint to be two times the square root of three we can
Dialogue: 0,0:06:31.83,0:06:33.56,Default,,0000,0000,0000,,verify that this works
Dialogue: 0,0:06:33.56,0:06:38.28,Default,,0000,0000,0000,,if you have this side squared so you have let\Nme write it down two times the square root of
Dialogue: 0,0:06:38.28,0:06:40.04,Default,,0000,0000,0000,,three squared
Dialogue: 0,0:06:40.04,0:06:42.93,Default,,0000,0000,0000,,plus two squared is equal to what
Dialogue: 0,0:06:42.93,0:06:43.89,Default,,0000,0000,0000,,this is
Dialogue: 0,0:06:43.89,0:06:47.12,Default,,0000,0000,0000,,two there's going to be four times three
Dialogue: 0,0:06:47.12,0:06:49.55,Default,,0000,0000,0000,,four times three plus four
Dialogue: 0,0:06:49.55,0:06:54.62,Default,,0000,0000,0000,,and this is going to be equal to twelve plus\Nfour is equal to sixteen and sixteen is indeed
Dialogue: 0,0:06:54.62,0:06:57.73,Default,,0000,0000,0000,,four squared so this does equal four squared
Dialogue: 0,0:06:57.73,0:07:02.42,Default,,0000,0000,0000,,it does equal four squared it satisfies the pythagorean theorem
Dialogue: 0,0:07:02.42,0:07:06.53,Default,,0000,0000,0000,,and if you remember some of your work from thirty\Nsixty ninety triangles that you might have
Dialogue: 0,0:07:06.53,0:07:09.05,Default,,0000,0000,0000,,learned in geometry you might recognize that\Nthis
Dialogue: 0,0:07:09.05,0:07:13.03,Default,,0000,0000,0000,,is a thirty sixty ninety triangle this\Nright here is our right angle i should have
Dialogue: 0,0:07:13.03,0:07:16.22,Default,,0000,0000,0000,,drawn it from the get go to show that this\Nis a right triangle
Dialogue: 0,0:07:16.22,0:07:20.21,Default,,0000,0000,0000,,this angle right over here is our thirty degree\Nangle
Dialogue: 0,0:07:20.21,0:07:24.43,Default,,0000,0000,0000,,and then this angle up here, this angle up here\Nis
Dialogue: 0,0:07:24.43,0:07:26.02,Default,,0000,0000,0000,,a sixty degree angle
Dialogue: 0,0:07:26.02,0:07:28.14,Default,,0000,0000,0000,,and it's a thirty sixteen ninety because
Dialogue: 0,0:07:28.14,0:07:31.99,Default,,0000,0000,0000,,the side opposite the thirty degrees is half the hypotenuse
Dialogue: 0,0:07:31.99,0:07:36.65,Default,,0000,0000,0000,,and then the side opposite the sixty degrees\Nis a squared three times the other side
Dialogue: 0,0:07:36.65,0:07:38.28,Default,,0000,0000,0000,,that's not the hypotenuse
Dialogue: 0,0:07:38.28,0:07:41.91,Default,,0000,0000,0000,,so that's that we're not gonna this isn't supposed to be a review of thirty sixty ninety triangles
Dialogue: 0,0:07:41.91,0:07:43.11,Default,,0000,0000,0000,,although i just did it
Dialogue: 0,0:07:43.11,0:07:46.83,Default,,0000,0000,0000,,let's actually find the trig ratios\Nfor the different angles
Dialogue: 0,0:07:46.83,0:07:48.08,Default,,0000,0000,0000,,so if i were to ask you
Dialogue: 0,0:07:48.08,0:07:51.06,Default,,0000,0000,0000,,or if anyone were to ask you what is
Dialogue: 0,0:07:51.06,0:07:54.39,Default,,0000,0000,0000,,what is the sine of thirty degrees
Dialogue: 0,0:07:54.39,0:07:58.52,Default,,0000,0000,0000,,and remember thirty degrees is one of the\Nangles in this triangle but it would apply
Dialogue: 0,0:07:58.52,0:08:01.52,Default,,0000,0000,0000,,whenever you have a thirty degree angle and\Nyou're dealing with the right triangle we'll
Dialogue: 0,0:08:01.52,0:08:04.97,Default,,0000,0000,0000,,have broader definitions in the future but\Nif you say sine of thirty degrees
Dialogue: 0,0:08:04.97,0:08:10.10,Default,,0000,0000,0000,,hey this ain't gold right over here is thirty\Ndegrees so i can use this right triangle
Dialogue: 0,0:08:10.10,0:08:12.85,Default,,0000,0000,0000,,and we just have to remember soh cah toa
Dialogue: 0,0:08:12.85,0:08:14.44,Default,,0000,0000,0000,,rewrite it so
Dialogue: 0,0:08:14.44,0:08:15.95,Default,,0000,0000,0000,,cah
Dialogue: 0,0:08:15.95,0:08:17.27,Default,,0000,0000,0000,,toa
Dialogue: 0,0:08:17.27,0:08:22.16,Default,,0000,0000,0000,,sine tells us soh tells us what to do with sine. sine is opposite over hypotenuse.
Dialogue: 0,0:08:23.05,0:08:26.20,Default,,0000,0000,0000,,sine of thirty degrees is the opposite side
Dialogue: 0,0:08:26.20,0:08:29.28,Default,,0000,0000,0000,,that is the opposite side which is two
Dialogue: 0,0:08:29.28,0:08:32.15,Default,,0000,0000,0000,,over the hypotenuse. the hypotenuse here is four.
Dialogue: 0,0:08:32.15,0:08:35.80,Default,,0000,0000,0000,,it is two fourths which is the same thing as\None-half
Dialogue: 0,0:08:35.80,0:08:39.02,Default,,0000,0000,0000,,sine of thirty degrees you'll see is always going\Nto be equal
Dialogue: 0,0:08:39.02,0:08:40.76,Default,,0000,0000,0000,,to one-half
Dialogue: 0,0:08:40.76,0:08:42.19,Default,,0000,0000,0000,,now what is
Dialogue: 0,0:08:42.19,0:08:43.91,Default,,0000,0000,0000,,the cosine
Dialogue: 0,0:08:43.91,0:08:45.98,Default,,0000,0000,0000,,what is the cosine of
Dialogue: 0,0:08:45.98,0:08:47.16,Default,,0000,0000,0000,,thirty degrees
Dialogue: 0,0:08:47.16,0:08:49.97,Default,,0000,0000,0000,,once again go back to soh cah toa.
Dialogue: 0,0:08:49.97,0:08:56.07,Default,,0000,0000,0000,,the cah tells us what to do with cosine. cosine is adjacent over hypotenuse
Dialogue: 0,0:08:56.07,0:08:59.94,Default,,0000,0000,0000,,so for looking at the thirty degree angle\Nit's the adjacent this right over here is
Dialogue: 0,0:08:59.94,0:09:01.64,Default,,0000,0000,0000,,adjacent it's right next to it
Dialogue: 0,0:09:01.64,0:09:02.96,Default,,0000,0000,0000,,it's not the hypotenuse
Dialogue: 0,0:09:02.96,0:09:06.79,Default,,0000,0000,0000,,it's the adjacent over the hypotenuse so\Nit's two
Dialogue: 0,0:09:06.79,0:09:08.78,Default,,0000,0000,0000,,square roots of three
Dialogue: 0,0:09:08.78,0:09:10.32,Default,,0000,0000,0000,,adjacent
Dialogue: 0,0:09:10.32,0:09:11.30,Default,,0000,0000,0000,,over
Dialogue: 0,0:09:11.30,0:09:13.82,Default,,0000,0000,0000,,over the hypotenuse over four
Dialogue: 0,0:09:13.82,0:09:19.29,Default,,0000,0000,0000,,or if we simplify that we divide the numerator and the denominator by two it's the square root of three
Dialogue: 0,0:09:19.29,0:09:20.78,Default,,0000,0000,0000,,over two
Dialogue: 0,0:09:20.78,0:09:23.20,Default,,0000,0000,0000,,finally let's do
Dialogue: 0,0:09:23.20,0:09:25.88,Default,,0000,0000,0000,,the tangent
Dialogue: 0,0:09:25.88,0:09:27.85,Default,,0000,0000,0000,,tangent of thirty degrees
Dialogue: 0,0:09:27.85,0:09:29.18,Default,,0000,0000,0000,,we go back to soh cah toa
Dialogue: 0,0:09:29.18,0:09:30.08,Default,,0000,0000,0000,,soh cah toa
Dialogue: 0,0:09:30.08,0:09:34.90,Default,,0000,0000,0000,,toa tells us what to do with tangent\Nit's opposite over adjacent
Dialogue: 0,0:09:34.90,0:09:38.86,Default,,0000,0000,0000,,you go to the thirty degree angle because that's what we care about, tangent of thirty
Dialogue: 0,0:09:38.86,0:09:42.76,Default,,0000,0000,0000,,tangent of thirty opposite is two
Dialogue: 0,0:09:42.76,0:09:47.15,Default,,0000,0000,0000,,opposite is two and the adjacent is two square roots of three it's right next to it it's adjacent
Dialogue: 0,0:09:47.15,0:09:47.83,Default,,0000,0000,0000,,to it
Dialogue: 0,0:09:47.83,0:09:49.43,Default,,0000,0000,0000,,adjacent means next to
Dialogue: 0,0:09:49.43,0:09:51.72,Default,,0000,0000,0000,,so two square roots of three
Dialogue: 0,0:09:51.72,0:09:53.11,Default,,0000,0000,0000,,so this is equal to
Dialogue: 0,0:09:53.11,0:09:56.82,Default,,0000,0000,0000,,the twos cancel out one over the square root\Nof three
Dialogue: 0,0:09:56.82,0:10:00.34,Default,,0000,0000,0000,,or we could multiply the numerator and the denominator\Nby the square root of three
Dialogue: 0,0:10:00.34,0:10:01.74,Default,,0000,0000,0000,,so we have
Dialogue: 0,0:10:01.74,0:10:03.29,Default,,0000,0000,0000,,square root of three
Dialogue: 0,0:10:03.29,0:10:05.20,Default,,0000,0000,0000,,over square root of three
Dialogue: 0,0:10:05.20,0:10:09.60,Default,,0000,0000,0000,,and so this is going to be equal to the numerator\Nsquare root of three and then the denominator
Dialogue: 0,0:10:09.60,0:10:14.90,Default,,0000,0000,0000,,right over here is just going to be three so\Nthats we've rationalized a square root of three
Dialogue: 0,0:10:14.90,0:10:15.89,Default,,0000,0000,0000,,over three
Dialogue: 0,0:10:15.89,0:10:16.72,Default,,0000,0000,0000,,fair enough
Dialogue: 0,0:10:16.72,0:10:20.50,Default,,0000,0000,0000,,now lets use the same triangle to figure out the\Ntrig ratios for the sixty degrees
Dialogue: 0,0:10:20.50,0:10:23.20,Default,,0000,0000,0000,,since we've already drawn it
Dialogue: 0,0:10:23.20,0:10:24.89,Default,,0000,0000,0000,,so what is
Dialogue: 0,0:10:24.89,0:10:30.58,Default,,0000,0000,0000,,what is in the sine of the sixty degrees and i think you're hopefully getting the hang of it now
Dialogue: 0,0:10:30.58,0:10:35.48,Default,,0000,0000,0000,,sine is opposite over adjacent. soh from the soh cah toa. from the sixty degree angle what side\N
Dialogue: 0,0:10:35.48,0:10:36.76,Default,,0000,0000,0000,,is opposite
Dialogue: 0,0:10:36.76,0:10:42.92,Default,,0000,0000,0000,,what opens out into the two square roots of three\Nso the opposite side is two square roots of three
Dialogue: 0,0:10:42.92,0:10:47.88,Default,,0000,0000,0000,,and from the sixty degree angle the adj-oh sorry its the
Dialogue: 0,0:10:47.88,0:10:54.42,Default,,0000,0000,0000,,opposite over hypotenuse, don't want to confuse you.
Dialogue: 0,0:10:54.42,0:10:58.75,Default,,0000,0000,0000,,so it is opposite over hypotenuse
Dialogue: 0,0:10:58.75,0:11:00.00,Default,,0000,0000,0000,,so it's two square roots of three over four. four is the hypotenuse.
Dialogue: 0,0:11:00.00,0:11:03.14,Default,,0000,0000,0000,,so it is equal to, this simplifies to square root of three over two.
Dialogue: 0,0:11:03.14,0:11:05.58,Default,,0000,0000,0000,,what is the cosine of sixty degrees. cosine of sixty degrees.
Dialogue: 0,0:11:05.58,0:11:10.33,Default,,0000,0000,0000,,so remember soh cah toa. cosine is adjacent over hypotenuse.
Dialogue: 0,0:11:10.33,0:11:15.07,Default,,0000,0000,0000,,adjacent is the two sides right next to the sixty degree angle so it's two
Dialogue: 0,0:11:15.07,0:11:17.92,Default,,0000,0000,0000,,over the hypotenuse which is four
Dialogue: 0,0:11:17.92,0:11:19.90,Default,,0000,0000,0000,,so this is equal to
Dialogue: 0,0:11:19.90,0:11:20.86,Default,,0000,0000,0000,,one-half
Dialogue: 0,0:11:20.86,0:11:22.12,Default,,0000,0000,0000,,and then finally
Dialogue: 0,0:11:22.12,0:11:24.46,Default,,0000,0000,0000,,what is the tangent, what is the tangent
Dialogue: 0,0:11:26.00,0:11:27.83,Default,,0000,0000,0000,,of sixty degrees
Dialogue: 0,0:11:27.83,0:11:32.79,Default,,0000,0000,0000,,well tangent soh cah toa tangent is opposite\Nover adjacent
Dialogue: 0,0:11:32.79,0:11:34.22,Default,,0000,0000,0000,,opposite the sixty degrees
Dialogue: 0,0:11:34.22,0:11:36.13,Default,,0000,0000,0000,,is two square roots of three
Dialogue: 0,0:11:36.13,0:11:37.94,Default,,0000,0000,0000,,two square roots of three
Dialogue: 0,0:11:37.94,0:11:39.57,Default,,0000,0000,0000,,and adjacent to that
Dialogue: 0,0:11:39.57,0:11:43.02,Default,,0000,0000,0000,,adjacent to that
Dialogue: 0,0:11:43.02,0:11:45.47,Default,,0000,0000,0000,,is two
Dialogue: 0,0:11:45.47,0:11:48.75,Default,,0000,0000,0000,,adjacent to sixty degrees is two
Dialogue: 0,0:11:48.75,0:11:52.63,Default,,0000,0000,0000,,so its opposite over adjacent
Dialogue: 0,0:11:52.63,0:11:56.00,Default,,0000,0000,0000,,two square roots of three over two which is just equal to
Dialogue: 0,0:11:56.00,0:11:58.15,Default,,0000,0000,0000,,the square root of three
Dialogue: 0,0:11:58.15,0:12:01.75,Default,,0000,0000,0000,,And I just wanted to - look how these are related
Dialogue: 0,0:12:01.75,0:12:03.36,Default,,0000,0000,0000,,the sine of thirty degrees is the same as the cosine of sixty degrees
Dialogue: 0,0:12:03.36,0:12:04.98,Default,,0000,0000,0000,,and then these guys are the inverse of each other and i think if you think a little bit about this triangle
Dialogue: 0,0:12:05.44,0:12:09.52,Default,,0000,0000,0000,,it will start to make sense why. we'll keep extending\Nthis and give you a lot more practice in the next
Dialogue: 0,0:12:09.52,0:12:10.11,Default,,0000,0000,0000,,few videos