[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.80,0:00:03.02,Default,,0000,0000,0000,,Let's just do a ton of more examples,
Dialogue: 0,0:00:03.02,0:00:07.04,Default,,0000,0000,0000,,just so we make sure that we're getting this trig function thing down well.
Dialogue: 0,0:00:07.04,0:00:11.45,Default,,0000,0000,0000,,So let's construct ourselves some right triangles.
Dialogue: 0,0:00:11.45,0:00:13.67,Default,,0000,0000,0000,,Let's construct ourselves some right triangles,
Dialogue: 0,0:00:13.67,0:00:15.19,Default,,0000,0000,0000,,and I want to be very clear.
Dialogue: 0,0:00:15.19,0:00:18.04,Default,,0000,0000,0000,,The way I've defined it so far, this will only work in right triangles.\N
Dialogue: 0,0:00:18.04,0:00:23.48,Default,,0000,0000,0000,,So if you're trying to find the trig functions of angles that aren't part of right triangles,
Dialogue: 0,0:00:23.48,0:00:25.70,Default,,0000,0000,0000,,we're going to see that we're going to have to construct right triangles,
Dialogue: 0,0:00:25.70,0:00:27.87,Default,,0000,0000,0000,,but let's just focus on the right triangles for now.
Dialogue: 0,0:00:27.87,0:00:31.34,Default,,0000,0000,0000,,So let's say that I have a triangle,
Dialogue: 0,0:00:31.34,0:00:33.90,Default,,0000,0000,0000,,where let's say this length down here is seven,
Dialogue: 0,0:00:33.90,0:00:37.76,Default,,0000,0000,0000,,and let's say the length of this side up here,
Dialogue: 0,0:00:37.76,0:00:39.45,Default,,0000,0000,0000,,let's say that that is four.
Dialogue: 0,0:00:39.45,0:00:42.52,Default,,0000,0000,0000,,Let's figure out what the hypotenuse over here is going to be.
Dialogue: 0,0:00:42.52,0:00:45.72,Default,,0000,0000,0000,,So we know -let's call the hypotenuse, "h"-
Dialogue: 0,0:00:45.72,0:00:52.20,Default,,0000,0000,0000,,we know that h squared is going to be equal to seven squared plus four squared,
Dialogue: 0,0:00:52.20,0:00:55.19,Default,,0000,0000,0000,,we know that from the Pythagorean theorem,
Dialogue: 0,0:00:55.19,0:00:57.47,Default,,0000,0000,0000,,that the hypotenuse squared is equal to
Dialogue: 0,0:00:57.47,0:01:01.97,Default,,0000,0000,0000,,the square of each of the sum of the squares of the other two sides.
Dialogue: 0,0:01:01.97,0:01:04.53,Default,,0000,0000,0000,,h squared is equal to seven squared plus four squared.
Dialogue: 0,0:01:04.53,0:01:09.78,Default,,0000,0000,0000,,So this is equal to forty-nine plus sixteen,
Dialogue: 0,0:01:09.78,0:01:11.80,Default,,0000,0000,0000,,forty-nine plus sixteen,
Dialogue: 0,0:01:11.80,0:01:18.55,Default,,0000,0000,0000,,forty nine plus ten is fifty-nine, plus six is sixty-five.
Dialogue: 0,0:01:18.55,0:01:21.11,Default,,0000,0000,0000,,It is sixty five. So this h squared,
Dialogue: 0,0:01:21.11,0:01:25.70,Default,,0000,0000,0000,,let me write: h squared -that's different shade of yellow-
Dialogue: 0,0:01:25.70,0:01:28.82,Default,,0000,0000,0000,,so we have h squared is equal to sixty-five.
Dialogue: 0,0:01:28.82,0:01:33.53,Default,,0000,0000,0000,,Did I do that right? Forty nine plus ten is fifty nine, plus another six is sixty-five,
Dialogue: 0,0:01:33.53,0:01:37.60,Default,,0000,0000,0000,,or we could say that h is equal to, if we take the square root of both sides,
Dialogue: 0,0:01:37.60,0:01:39.20,Default,,0000,0000,0000,,square root
Dialogue: 0,0:01:39.20,0:01:42.93,Default,,0000,0000,0000,,square root of sixty five. And we really can't simplify\Nthis at all.
Dialogue: 0,0:01:42.93,0:01:44.70,Default,,0000,0000,0000,,This is thirteen.
Dialogue: 0,0:01:44.70,0:01:47.46,Default,,0000,0000,0000,,This is the same thing as thirteen times five,\N
Dialogue: 0,0:01:47.46,0:01:50.39,Default,,0000,0000,0000,,both of those are not perfect squares and
Dialogue: 0,0:01:50.39,0:01:51.80,Default,,0000,0000,0000,,they're both prime so you can't simplify this any more.
Dialogue: 0,0:01:51.80,0:01:55.47,Default,,0000,0000,0000,,So this is equal to the square root of sixty five.
Dialogue: 0,0:01:55.47,0:02:02.11,Default,,0000,0000,0000,,Now let's find the trig, let's find the trig functions for this angle up here.
Dialogue: 0,0:02:02.11,0:02:05.46,Default,,0000,0000,0000,,Let's call that angle up there theta.
Dialogue: 0,0:02:05.46,0:02:06.53,Default,,0000,0000,0000,,So whenever you do it
Dialogue: 0,0:02:06.53,0:02:09.47,Default,,0000,0000,0000,,you always want to write down - at least for me it works out to write down -
Dialogue: 0,0:02:09.47,0:02:11.71,Default,,0000,0000,0000,,"soh cah toa".
Dialogue: 0,0:02:11.71,0:02:13.12,Default,,0000,0000,0000,,soh...
Dialogue: 0,0:02:13.12,0:02:16.46,Default,,0000,0000,0000,,...soh cah toa. I have these vague memories
Dialogue: 0,0:02:16.46,0:02:18.79,Default,,0000,0000,0000,,of my trigonometry teacher.
Dialogue: 0,0:02:18.79,0:02:21.29,Default,,0000,0000,0000,,Maybe I've read it in some book. I don't know - you know, some... about
Dialogue: 0,0:02:21.29,0:02:23.87,Default,,0000,0000,0000,,some type of indian princess named "soh cah toa" or whatever,
Dialogue: 0,0:02:23.87,0:02:26.12,Default,,0000,0000,0000,,but it's a very useful mnemonic,
Dialogue: 0,0:02:26.12,0:02:27.56,Default,,0000,0000,0000,,so we can apply "soh cah toa".
Dialogue: 0,0:02:27.56,0:02:31.05,Default,,0000,0000,0000,,Let's find, let's say we want to find the cosine.
Dialogue: 0,0:02:31.05,0:02:34.44,Default,,0000,0000,0000,,We want to find the cosine of our angle.
Dialogue: 0,0:02:34.44,0:02:37.96,Default,,0000,0000,0000,,We wanna find the cosine of our angle, you say: "soh cah toa!"
Dialogue: 0,0:02:37.96,0:02:40.80,Default,,0000,0000,0000,,So the "cah". "Cah" tells us what to do with cosine,
Dialogue: 0,0:02:40.80,0:02:43.03,Default,,0000,0000,0000,,the "cah" part tells us
Dialogue: 0,0:02:43.03,0:02:46.37,Default,,0000,0000,0000,,that cosine is adjacent over hypotenuse.
Dialogue: 0,0:02:46.37,0:02:51.43,Default,,0000,0000,0000,,Cosine is equal to adjacent over hypotenuse.
Dialogue: 0,0:02:51.43,0:02:55.80,Default,,0000,0000,0000,,So let's look over here to theta; what side is adjacent?
Dialogue: 0,0:02:55.80,0:02:57.70,Default,,0000,0000,0000,,Well we know that the hypotenuse,
Dialogue: 0,0:02:57.70,0:03:00.77,Default,,0000,0000,0000,,we know that that hypotenuse is this side over here.
Dialogue: 0,0:03:00.77,0:03:04.76,Default,,0000,0000,0000,,So it can't be that side. The only other side that's kind of adjacent to it that
Dialogue: 0,0:03:04.76,0:03:07.13,Default,,0000,0000,0000,,isn't the hypotenuse, is this four.
Dialogue: 0,0:03:07.13,0:03:10.47,Default,,0000,0000,0000,,So the adjacent side over here, that side is,
Dialogue: 0,0:03:10.47,0:03:14.37,Default,,0000,0000,0000,,it's literally right next to the angle,
Dialogue: 0,0:03:14.37,0:03:15.75,Default,,0000,0000,0000,,it's one of the sides that kind of forms the angle
Dialogue: 0,0:03:15.75,0:03:17.13,Default,,0000,0000,0000,,it's four over the hypotenuse.
Dialogue: 0,0:03:17.13,0:03:21.11,Default,,0000,0000,0000,,The hypotenuse we already know is square root\Nof sixty-five.
Dialogue: 0,0:03:21.11,0:03:25.38,Default,,0000,0000,0000,,so it's four over the square root of sixty-five.
Dialogue: 0,0:03:25.38,0:03:29.14,Default,,0000,0000,0000,,And sometimes people will want you to rationalize the denominator which means
Dialogue: 0,0:03:29.14,0:03:32.62,Default,,0000,0000,0000,,they don't like to have an irrational number in the denominator,
Dialogue: 0,0:03:32.62,0:03:35.23,Default,,0000,0000,0000,,like the square root of sixty five,
Dialogue: 0,0:03:35.23,0:03:39.36,Default,,0000,0000,0000,,and if they - if you wanna rewrite this without a irrational number in the denominator,
Dialogue: 0,0:03:39.36,0:03:41.63,Default,,0000,0000,0000,,you can multiply the numerator and the denominator
Dialogue: 0,0:03:41.63,0:03:43.31,Default,,0000,0000,0000,,by the square root of sixty-five.
Dialogue: 0,0:03:43.31,0:03:45.09,Default,,0000,0000,0000,,This clearly will not change the number,
Dialogue: 0,0:03:45.09,0:03:48.12,Default,,0000,0000,0000,,because we're multiplying it by something over itself,
Dialogue: 0,0:03:48.12,0:03:49.11,Default,,0000,0000,0000,,so we're multiplying the number by one.
Dialogue: 0,0:03:49.11,0:03:52.78,Default,,0000,0000,0000,,That won't change the number, but at least it gets rid of the irrational number in the denominator.
Dialogue: 0,0:03:52.78,0:03:54.13,Default,,0000,0000,0000,,So the numerator becomes
Dialogue: 0,0:03:54.13,0:03:57.80,Default,,0000,0000,0000,,four times the square root of sixty-five,
Dialogue: 0,0:03:57.80,0:04:03.46,Default,,0000,0000,0000,,and the denominator, square root of 65 times square root of 65, is just going to be 65.
Dialogue: 0,0:04:03.46,0:04:07.13,Default,,0000,0000,0000,,We didn't get rid of the irrational number, it's still there, but it's now in the numerator.
Dialogue: 0,0:04:07.13,0:04:09.78,Default,,0000,0000,0000,,Now let's do the other trig functions
Dialogue: 0,0:04:09.78,0:04:12.40,Default,,0000,0000,0000,,or at least the other core trig functions.
Dialogue: 0,0:04:12.40,0:04:14.40,Default,,0000,0000,0000,,We'll learn in the future that there's actually a ton of them
Dialogue: 0,0:04:14.40,0:04:15.44,Default,,0000,0000,0000,,but they're all derived from these.
Dialogue: 0,0:04:15.44,0:04:19.73,Default,,0000,0000,0000,,so let's think about what the sign of theta is. Once again\Ngo to "soh cah toa".
Dialogue: 0,0:04:19.73,0:04:25.47,Default,,0000,0000,0000,,The "soh" tells what to do with sine. Sine is opposite over hypotenuse.
Dialogue: 0,0:04:25.47,0:04:29.20,Default,,0000,0000,0000,,Sine is equal to opposite over hypotenuse.
Dialogue: 0,0:04:29.20,0:04:31.37,Default,,0000,0000,0000,,Sine is opposite over hypotenuse.
Dialogue: 0,0:04:31.37,0:04:34.39,Default,,0000,0000,0000,,So for this angle what side is opposite?
Dialogue: 0,0:04:34.39,0:04:38.43,Default,,0000,0000,0000,,We just go opposite it, what it opens into, it's opposite the seven
Dialogue: 0,0:04:38.43,0:04:41.20,Default,,0000,0000,0000,,so the opposite side is the seven.
Dialogue: 0,0:04:41.20,0:04:44.47,Default,,0000,0000,0000,,This is, right here - that is the opposite side
Dialogue: 0,0:04:44.47,0:04:47.80,Default,,0000,0000,0000,,and then the hypotenuse, it's opposite over hypotenuse.
Dialogue: 0,0:04:47.80,0:04:51.11,Default,,0000,0000,0000,,The hypotenuse is the square root of sixty-five.
Dialogue: 0,0:04:51.11,0:04:52.97,Default,,0000,0000,0000,,Square root of sixty-five.
Dialogue: 0,0:04:52.97,0:04:55.13,Default,,0000,0000,0000,,and once again if we wanted to rationalize this,\N
Dialogue: 0,0:04:55.13,0:04:59.93,Default,,0000,0000,0000,,we could multiply times the square root of 65 over the square root of 65
Dialogue: 0,0:04:59.93,0:05:04.30,Default,,0000,0000,0000,,and the the numerator, we will get seven square root of 65
Dialogue: 0,0:05:04.30,0:05:07.97,Default,,0000,0000,0000,,and in the denominator we will get just sixty-five again.
Dialogue: 0,0:05:07.97,0:05:10.47,Default,,0000,0000,0000,,Now let's do tangent!
Dialogue: 0,0:05:10.47,0:05:12.80,Default,,0000,0000,0000,,Let us do tangent.
Dialogue: 0,0:05:12.80,0:05:14.79,Default,,0000,0000,0000,,So if i ask you the tangent
Dialogue: 0,0:05:14.79,0:05:17.39,Default,,0000,0000,0000,,of - the tangent of theta
Dialogue: 0,0:05:17.39,0:05:20.78,Default,,0000,0000,0000,,once again go back to "soh cah toa".
Dialogue: 0,0:05:20.78,0:05:23.11,Default,,0000,0000,0000,,The toa part tells us what to do with tangent
Dialogue: 0,0:05:23.11,0:05:24.80,Default,,0000,0000,0000,,it tells us...
Dialogue: 0,0:05:24.80,0:05:27.05,Default,,0000,0000,0000,,it tells us that tangent
Dialogue: 0,0:05:27.05,0:05:29.87,Default,,0000,0000,0000,,is equal to opposite over adjacent
Dialogue: 0,0:05:29.87,0:05:33.14,Default,,0000,0000,0000,,is equal to opposite over
Dialogue: 0,0:05:33.14,0:05:35.87,Default,,0000,0000,0000,,opposite over adjacent
Dialogue: 0,0:05:35.87,0:05:38.71,Default,,0000,0000,0000,,So for this angle, what is opposite? We've already figured it out.
Dialogue: 0,0:05:38.71,0:05:41.12,Default,,0000,0000,0000,,it's seven. It opens into the seven.
Dialogue: 0,0:05:41.12,0:05:42.53,Default,,0000,0000,0000,,It is opposite the seven.
Dialogue: 0,0:05:42.53,0:05:46.37,Default,,0000,0000,0000,,So it's seven over what side is adjacent.
Dialogue: 0,0:05:46.37,0:05:48.20,Default,,0000,0000,0000,,well this four is adjacent.
Dialogue: 0,0:05:48.20,0:05:51.30,Default,,0000,0000,0000,,This four is adjacent. So the adjacent side is four.
Dialogue: 0,0:05:51.30,0:05:54.33,Default,,0000,0000,0000,,so it's seven over four,
Dialogue: 0,0:05:54.33,0:05:56.13,Default,,0000,0000,0000,,and we're done.
Dialogue: 0,0:05:56.13,0:05:59.38,Default,,0000,0000,0000,,We figured out all of the trig ratios for theta. let's do another one.
Dialogue: 0,0:05:59.38,0:06:00.42,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:06:00.42,0:06:02.72,Default,,0000,0000,0000,,i'll make it a little bit concrete 'cause right now we've been saying,
Dialogue: 0,0:06:02.72,0:06:06.43,Default,,0000,0000,0000,,"oh, what's tangent of x, tangent of theta." let's make it a little bit more concrete.
Dialogue: 0,0:06:06.43,0:06:08.43,Default,,0000,0000,0000,,Let's say...
Dialogue: 0,0:06:08.43,0:06:10.80,Default,,0000,0000,0000,,let's say, let me draw another right triangle,
Dialogue: 0,0:06:10.80,0:06:13.77,Default,,0000,0000,0000,,that's another right triangle here.
Dialogue: 0,0:06:13.77,0:06:17.53,Default,,0000,0000,0000,,Everything we're dealing with, these are going to be right triangles.
Dialogue: 0,0:06:17.53,0:06:21.11,Default,,0000,0000,0000,,let's say the hypotenuse has length four,
Dialogue: 0,0:06:21.11,0:06:26.36,Default,,0000,0000,0000,,let's say that this side over here has length two,
Dialogue: 0,0:06:26.36,0:06:31.79,Default,,0000,0000,0000,,and let's say that this length over here is going to be two times the square root of three.
Dialogue: 0,0:06:31.79,0:06:33.46,Default,,0000,0000,0000,,We can verify that this works.
Dialogue: 0,0:06:33.46,0:06:36.47,Default,,0000,0000,0000,,If you have this side squared, so you have - let me write it down -
Dialogue: 0,0:06:36.47,0:06:38.80,Default,,0000,0000,0000,,two times the square root of three squared
Dialogue: 0,0:06:38.80,0:06:42.47,Default,,0000,0000,0000,,plus two squared, is equal to what?
Dialogue: 0,0:06:42.47,0:06:46.47,Default,,0000,0000,0000,,this is two. There's going to be four times three.
Dialogue: 0,0:06:46.47,0:06:49.76,Default,,0000,0000,0000,,four times three plus four,
Dialogue: 0,0:06:49.76,0:06:53.48,Default,,0000,0000,0000,,and this is going to be equal to twelve plus four is equal to sixteen
Dialogue: 0,0:06:53.48,0:06:57.80,Default,,0000,0000,0000,,and sixteen is indeed four squared. So this does equal four squared,
Dialogue: 0,0:06:57.80,0:07:01.79,Default,,0000,0000,0000,,it does equal four squared. It satisfies the pythagorean theorem
Dialogue: 0,0:07:01.79,0:07:06.13,Default,,0000,0000,0000,,and if you remember some of your work from 30 60 90 triangles
Dialogue: 0,0:07:06.13,0:07:07.78,Default,,0000,0000,0000,,that you might have learned in geometry,
Dialogue: 0,0:07:07.78,0:07:11.45,Default,,0000,0000,0000,,you might recognize that this is a 30 60 90 triangle.\N
Dialogue: 0,0:07:11.45,0:07:13.13,Default,,0000,0000,0000,,This right here is our right angle,
Dialogue: 0,0:07:13.13,0:07:15.87,Default,,0000,0000,0000,,- i should have drawn it from the get go to show that this is a right triangle -
Dialogue: 0,0:07:15.87,0:07:20.37,Default,,0000,0000,0000,,this angle right over here is our thirty degree angle
Dialogue: 0,0:07:20.37,0:07:23.38,Default,,0000,0000,0000,,and then this angle up here, this angle up here is
Dialogue: 0,0:07:23.38,0:07:26.12,Default,,0000,0000,0000,,a sixty degree angle,
Dialogue: 0,0:07:26.12,0:07:27.80,Default,,0000,0000,0000,,and it's a thirty sixteen ninety because
Dialogue: 0,0:07:27.80,0:07:31.79,Default,,0000,0000,0000,,the side opposite the thirty degrees is half the hypotenuse
Dialogue: 0,0:07:31.79,0:07:36.80,Default,,0000,0000,0000,,and then the side opposite the 60 degrees is a squared of 3 times the other side
Dialogue: 0,0:07:36.80,0:07:38.43,Default,,0000,0000,0000,,that's not the hypotenuse.
Dialogue: 0,0:07:38.43,0:07:40.16,Default,,0000,0000,0000,,So that said, we're not gonna ...
Dialogue: 0,0:07:40.16,0:07:43.42,Default,,0000,0000,0000,,this isn't supposed to be a review of 30 60 90 triangles although i just did it.
Dialogue: 0,0:07:43.42,0:07:46.93,Default,,0000,0000,0000,,Let's actually find the trig ratios for the different angles.
Dialogue: 0,0:07:46.93,0:07:51.30,Default,,0000,0000,0000,,So if i were to ask you or if anyone were to ask you, what is...
Dialogue: 0,0:07:51.30,0:07:54.64,Default,,0000,0000,0000,,what is the sine of thirty degrees?
Dialogue: 0,0:07:54.64,0:07:58.45,Default,,0000,0000,0000,,and remember 30 degrees is one of the angles in this triangle but it would apply
Dialogue: 0,0:07:58.45,0:08:01.70,Default,,0000,0000,0000,,whenever you have a 30 degree angle and you're dealing with the right triangle.
Dialogue: 0,0:08:01.70,0:08:05.14,Default,,0000,0000,0000,,We'll have broader definitions in the future but if you say sine of thirty degrees,
Dialogue: 0,0:08:05.14,0:08:09.04,Default,,0000,0000,0000,,hey, this angle right over here is thirty degrees so i can use this right triangle,
Dialogue: 0,0:08:09.04,0:08:12.13,Default,,0000,0000,0000,,and we just have to remember "soh cah toa"
Dialogue: 0,0:08:12.13,0:08:17.12,Default,,0000,0000,0000,,We rewrite it. soh, cah, toa.
Dialogue: 0,0:08:17.12,0:08:22.78,Default,,0000,0000,0000,,"sine tells us" (correction). soh tells us what to do with sine. sine is opposite over hypotenuse.
Dialogue: 0,0:08:22.78,0:08:26.36,Default,,0000,0000,0000,,sine of thirty degrees is the opposite side,
Dialogue: 0,0:08:26.36,0:08:30.72,Default,,0000,0000,0000,,that is the opposite side which is two over the hypotenuse.
Dialogue: 0,0:08:30.72,0:08:32.40,Default,,0000,0000,0000,,The hypotenuse here is four.
Dialogue: 0,0:08:32.40,0:08:35.65,Default,,0000,0000,0000,,it is two fourths which is the same thing as one-half.
Dialogue: 0,0:08:35.65,0:08:40.80,Default,,0000,0000,0000,,sine of thirty degrees you'll see is always going to be equal to one-half.
Dialogue: 0,0:08:40.80,0:08:44.14,Default,,0000,0000,0000,,now what is the cosine?
Dialogue: 0,0:08:44.14,0:08:46.87,Default,,0000,0000,0000,,What is the cosine of thirty degrees?
Dialogue: 0,0:08:46.87,0:08:50.14,Default,,0000,0000,0000,,Once again go back to "soh cah toa".
Dialogue: 0,0:08:50.14,0:08:52.64,Default,,0000,0000,0000,,The cah tells us what to do with cosine.
Dialogue: 0,0:08:52.64,0:08:56.03,Default,,0000,0000,0000,,Cosine is adjacent over hypotenuse.
Dialogue: 0,0:08:56.03,0:08:59.05,Default,,0000,0000,0000,,So for looking at the thirty degree angle it's the adjacent.
Dialogue: 0,0:08:59.05,0:09:01.79,Default,,0000,0000,0000,,This, right over here is adjacent. it's right next to it.
Dialogue: 0,0:09:01.79,0:09:05.47,Default,,0000,0000,0000,,it's not the hypotenuse. it's the adjacent over the hypotenuse.
Dialogue: 0,0:09:05.47,0:09:09.13,Default,,0000,0000,0000,,so it's two square roots of three
Dialogue: 0,0:09:09.13,0:09:13.63,Default,,0000,0000,0000,,adjacent over...over the hypotenuse, over four.
Dialogue: 0,0:09:13.63,0:09:16.98,Default,,0000,0000,0000,,or if we simplify that, we divide the numerator and the denominator by two
Dialogue: 0,0:09:16.98,0:09:20.65,Default,,0000,0000,0000,,it's the square root of three over two.
Dialogue: 0,0:09:20.65,0:09:22.78,Default,,0000,0000,0000,,Finally, let's do the tangent.
Dialogue: 0,0:09:22.78,0:09:27.80,Default,,0000,0000,0000,,The tangent of thirty degrees,
Dialogue: 0,0:09:27.80,0:09:30.30,Default,,0000,0000,0000,,we go back to "soh cah toa".
Dialogue: 0,0:09:30.30,0:09:31.70,Default,,0000,0000,0000,,soh cah toa
Dialogue: 0,0:09:31.70,0:09:34.80,Default,,0000,0000,0000,,toa tells us what to do with tangent. It's opposite over adjacent
Dialogue: 0,0:09:34.80,0:09:38.80,Default,,0000,0000,0000,,you go to the 30 degree angle because that's what we care about, tangent of 30.
Dialogue: 0,0:09:38.80,0:09:42.10,Default,,0000,0000,0000,,tangent of thirty. Opposite is two,
Dialogue: 0,0:09:42.10,0:09:46.20,Default,,0000,0000,0000,,opposite is two and the adjacent is two square roots of three.
Dialogue: 0,0:09:46.20,0:09:48.04,Default,,0000,0000,0000,,It's right next to it. It's adjacent to it.
Dialogue: 0,0:09:48.04,0:09:49.44,Default,,0000,0000,0000,,adjacent means next to.
Dialogue: 0,0:09:49.44,0:09:52.04,Default,,0000,0000,0000,,so two square roots of three
Dialogue: 0,0:09:52.04,0:09:54.45,Default,,0000,0000,0000,,so this is equal to... the twos cancel out
Dialogue: 0,0:09:54.45,0:09:56.78,Default,,0000,0000,0000,,one over the square root of three
Dialogue: 0,0:09:56.78,0:10:00.72,Default,,0000,0000,0000,,or we could multiply the numerator and the denominator by the square root of three.
Dialogue: 0,0:10:00.72,0:10:05.37,Default,,0000,0000,0000,,So we have square root of three over square root of three
Dialogue: 0,0:10:05.37,0:10:08.80,Default,,0000,0000,0000,,and so this is going to be equal to the numerator square root of three and then
Dialogue: 0,0:10:08.80,0:10:12.47,Default,,0000,0000,0000,,the denominator right over here is just going to be three.
Dialogue: 0,0:10:12.47,0:10:15.80,Default,,0000,0000,0000,,So that we've rationalized a square root of three over three.
Dialogue: 0,0:10:15.80,0:10:17.44,Default,,0000,0000,0000,,Fair enough.
Dialogue: 0,0:10:17.44,0:10:20.69,Default,,0000,0000,0000,,Now lets use the same triangle to figure out the trig ratios for the sixty degrees,
Dialogue: 0,0:10:20.69,0:10:22.46,Default,,0000,0000,0000,,since we've already drawn it.
Dialogue: 0,0:10:22.46,0:10:28.33,Default,,0000,0000,0000,,so what is... what is the sine of the sixty degrees?
Dialogue: 0,0:10:28.33,0:10:30.17,Default,,0000,0000,0000,,and i think you're hopefully getting the hang of it now.
Dialogue: 0,0:10:30.17,0:10:34.25,Default,,0000,0000,0000,,Sine is opposite over adjacent. soh from the "soh cah toa". \N
Dialogue: 0,0:10:34.25,0:10:36.67,Default,,0000,0000,0000,,for the sixty degree angle what side is opposite?
Dialogue: 0,0:10:36.67,0:10:39.32,Default,,0000,0000,0000,,what opens out into the two square roots of three,\N
Dialogue: 0,0:10:39.32,0:10:42.57,Default,,0000,0000,0000,,so the opposite side is two square roots of three,
Dialogue: 0,0:10:42.57,0:10:45.31,Default,,0000,0000,0000,,and from the sixty degree angle the adj-oh sorry
Dialogue: 0,0:10:45.31,0:10:47.100,Default,,0000,0000,0000,,its the opposite over hypotenuse, don't want to confuse you.
Dialogue: 0,0:10:47.100,0:10:50.51,Default,,0000,0000,0000,,so it is opposite over hypotenuse
Dialogue: 0,0:10:50.51,0:10:54.32,Default,,0000,0000,0000,,so it's two square roots of three over four. four is the hypotenuse.
Dialogue: 0,0:10:54.32,0:10:59.98,Default,,0000,0000,0000,,so it is equal to, this simplifies to square root of three over two.
Dialogue: 0,0:10:59.98,0:11:05.51,Default,,0000,0000,0000,,What is the cosine of sixty degrees? cosine of sixty degrees.
Dialogue: 0,0:11:05.51,0:11:10.24,Default,,0000,0000,0000,,so remember "soh cah toa". cosine is adjacent over hypotenuse.
Dialogue: 0,0:11:10.24,0:11:13.67,Default,,0000,0000,0000,,adjacent is the two sides, right next to the sixty degree angle.
Dialogue: 0,0:11:13.67,0:11:17.91,Default,,0000,0000,0000,,So it's two over the hypotenuse which is four.
Dialogue: 0,0:11:17.91,0:11:20.97,Default,,0000,0000,0000,,So this is equal to one-half
Dialogue: 0,0:11:20.97,0:11:24.18,Default,,0000,0000,0000,,and then finally, what is the tangent?
Dialogue: 0,0:11:24.18,0:11:27.98,Default,,0000,0000,0000,,what is the tangent of sixty degrees?
Dialogue: 0,0:11:27.98,0:11:32.35,Default,,0000,0000,0000,,Well tangent, "soh cah toa". Tangent is opposite over adjacent
Dialogue: 0,0:11:32.35,0:11:34.67,Default,,0000,0000,0000,,opposite the sixty degrees
Dialogue: 0,0:11:34.67,0:11:36.40,Default,,0000,0000,0000,,is two square roots of three
Dialogue: 0,0:11:36.40,0:11:38.00,Default,,0000,0000,0000,,two square roots of three
Dialogue: 0,0:11:38.00,0:11:39.92,Default,,0000,0000,0000,,and adjacent to that
Dialogue: 0,0:11:39.92,0:11:42.73,Default,,0000,0000,0000,,adjacent to that is two.
Dialogue: 0,0:11:42.73,0:11:44.80,Default,,0000,0000,0000,,Adjacent to sixty degrees is two.
Dialogue: 0,0:11:44.80,0:11:48.65,Default,,0000,0000,0000,,So its opposite over adjacent, two square roots of three over two
Dialogue: 0,0:11:48.65,0:11:52.64,Default,,0000,0000,0000,,which is just equal to the square root of three.
Dialogue: 0,0:11:52.64,0:11:54.64,Default,,0000,0000,0000,,And I just wanted to -look how these are related-
Dialogue: 0,0:11:54.64,0:11:57.98,Default,,0000,0000,0000,,the sine of thirty degrees is the same as the cosine of sixty degrees.
Dialogue: 0,0:11:57.98,0:12:01.33,Default,,0000,0000,0000,,The cosine of 30 degrees is the same thing as the sine of 60 degrees
Dialogue: 0,0:12:01.33,0:12:03.97,Default,,0000,0000,0000,,and then these guys are the inverse of each other
Dialogue: 0,0:12:03.97,0:12:05.64,Default,,0000,0000,0000,,and i think if you think a little bit about this triangle
Dialogue: 0,0:12:05.64,0:12:07.10,Default,,0000,0000,0000,,it will start to make sense why.
Dialogue: 0,0:12:07.10,0:12:08.46,Default,,0000,0000,0000,,we'll keep extending\Nthis and
Dialogue: 0,0:12:08.46,9:59:59.99,Default,,0000,0000,0000,,give you a lot more practice in the next few videos.