WEBVTT

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Let's just do a ton of more examples, just so we
make sure that we're getting

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this trig function thing down well.

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So let's construct ourselves some right triangles.

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Let's construct ourselves some right triangles, and I want to be very clear the way I've defined

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it so far will only work in right triangles,
so if you try to find

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the trig

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functions of angles that aren't part of right
triangles, we're goint to see a that we're going to have to construct right

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triangles, but let's just focus on the right triangles
for now.

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So let's say that I have a triangle, where
let's say this lengthy down here is seven,

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and let's say the length of this side up here, let's say that that is four.

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Let's figure out what the hypotenuse over here is going to be. So we know

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-let's call the hypotenuse "h"-

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we know that h squared is going to be equal
to seven squared plus four squared, we know

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that from of the Pythagorean theorem.

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That the hypotenuse squared is equal to

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the square of each of the - the sum of the
squares

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of the other two sides. Eight squared is equal to seven
squared plus four squared.

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So this is the equal to forty-nine

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plus sixteen,

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fourty-nine plus sixteen,

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forty nine plus ten is fifty-nine, plus
six is

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sixty-five. It is a sixty five so this h squared,

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let me right: h squared,

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that's different shade of yellow, so we have h squared is equal to

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sixty-five. Did I do that right? Forty nine plus ten is fifty nine, plus another six

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is sixty-five, or we could see that h is equal to, if we take the square root of

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both sides

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square root

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square root of sixty five. And we really can simplify
this at all

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this is thirteen

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this is the same thing is thirteen times five,
both of those are not perfect squares and

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they're both

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prime so you can't simplify this any more.

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So this is equal to the square root

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of sixty five.

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Now let's find the trig functions for this angle
up here, let's call that angle up there theta.

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So whenever you do it

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you always want to write down - at least for
me it works out to write down -

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"soh cah toa".

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soh...

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...soh cah toa. I have these vague memories

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of my

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trigonometry teacher, maybe I've read it in some
book, I don't know - you know about

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some type of indian princess named "soh cah toa" or whatever, but it's a very useful

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new monic, so we can apply "soh cah toa" to find

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let's say we want to find the cosine, we want to find the cosine of our angle,

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we wanna find the cosine of our angle, you
say: "soh cah toa!"

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So the "cah" tells us what to do with cosine,

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the "cah" part tells us

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that cosine is adjacent over hypotenuse.

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Cosine is equal to adjacent

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over hypotenuse.

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So let's look over here to theta; what side is adjacent?

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Well we know that the hypotenuse

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we know that that hypotenuse is this side over here

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so it can't be that side. The only
other side that's kind of adjacent to it that

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isn't the hypotenuse, is this four.

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So the adjacent side over here, that side is,

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it's right next to the angle, it's one of
the sides that kind of forms the angle

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it's four

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over the hypotenuse.

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The hypotenuse we already know, it's square root
of sixty-five, so it's four

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over

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the square root of sixty-five.

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And sometimes people will want you to rationalize
the denominator which means they don't like

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to have an irrational number in the denominator,
like the square root of sixty five

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and if they - if you wanna rewrite this without
the

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irrational number in the denominator, you can
multiply the numerator and the denominator

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by the square root of sixty-five.

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This clearly will not change the number, because we're multiplying it by something over itself, so we're

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multiplying the number by one. That won't change
the number, but at least it gets rid of the

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irrational number in the denominator. So the numerator
becomes

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four times the square root of sixty-five,

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and denominator square two sixty five times
square to sixty-five is just going to be sixty-five.

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We didn't get rid of the irrational number, it's still
there, but it's now in the numerator.

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now let's do the other trick functions

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carelessly said the court rick functions will
learn in the future that there's a few tumble

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but they're all derived from these

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fussing about the sign of state is once again
to go to so cut off

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the sole tells what to do it signed side of
the opposite over high positives

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sign

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is equal to

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opposite over hypothesize opposite over high
partners

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so for this and all tried as officer

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we just go

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opposite itworld opens into it's opposite
the seven

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so the opposite side is the seven this is

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right here that is the opposite side

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and then in the

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hypothalamus opposite overabundance of hypothesis
in the square root of sixty-five

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square root sixty-five

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and once again if we want to rationalize this
week a multiply times square in sixty five

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over the square to sixty-five

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numerator will get seven square roots of sixty-five
and in the denominator we will get jest

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sixty-five again

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knowledge do tangent

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let us do ten gente

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so if i ask you the tangent

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but ended up there

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once again go back to soak up

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toa the toll apart tells us what to do a tangent

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it tells us

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it tells us that tangent

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is equal to opposite over adjacent is equal
to opposite

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over

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opposite over ed to use it

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so for this and all

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what is opposite we've already figured it
out it's evident opens into the seventh opposite

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the seven

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so it's seven

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over website is adjacent

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well this for is adjacent

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this for is adjacent to the jason side is
four

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so it's seven

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over

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and were dot

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we figured out all of the trade ratios for
baidoa let's do it other one

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let's do another one on the colluded concrete
'cause right now we've been saying oh was

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tentative actress tens of their lives make
a little bit more concrete

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let's say

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let's say i mean drawn other right triangle

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list another right triangle here

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everything we're dealing with

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these are going to be right triangles

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let's say the high partners

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has the length

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let's say that the side over here

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has length too

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and let's say that this length overhears will
be to times the square root of three we can

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verify that this works

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if you have this aside squared so yet let
me write down two times the square root of

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three squared

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plus to squared is equal to what

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this is

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to there's going to be four times three

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four times three plus four

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and this is going to be equal to twelve plus
for the for the sixteen and sixteen is indeed

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four square so this does he call for squared

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it does equal foursquare it satisfies the
protagonist hero

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if you remember some of your work from thirty
sixty ninety triangles that you might have

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learned in geometry you might recognize that
this

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is eight thirty sixty ninety triangle this
right here is our right angle i should have

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drawn it from the get go to show that this
is the right triangle

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this angle right over here is our thirty degree
angle

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and then disable appear the single appears
is

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sixty degree angle

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and it's a pretty sixteen ninety because

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the side opposite the thirty degrees is half
of my partners

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and in the side opposite the sixty degrees
is a square to three times the other side

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that's not the hype on this

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so that's that we're not gonna the student
was peer review of thirty sixty ninety triangles

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although i just get it

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let's actually fifi and the trigger issues
for the different angles

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so if i were to ask you

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or if anyone would ask you what is

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what is the signed of thirty degrees

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and remember thirty degrees is one of the
eagles in this triangle but it would apply

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whenever you have a thirty degree angle and
you're dealing with the right rangel will

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have broader definitions of the future but
if you see a sign of thirty degrees

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hey this ain't gold right over here is thirty
degrees so i can use this right triangle

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and we should remember so catawba

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rewrite it so

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ka

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toa

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sign tells us more also tells us what to do
it signed side is opposite over hype rotten

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is

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sign up thirty degrees is the opposite side

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that is the opposite side which is to

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over the hard part is the hype on this year's
for

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it is to ford's which is the same thing as
one-half

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five thirty degrees you'll see is always going
to be equal

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to one-half

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now what is

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the duck cosign

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what is the co-signed of

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thirty degrees

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once again go back to seoul cut off

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the cod tells us what to do with co-sign co-sign
isn't jay sent over high popped in his

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so for looking at the thirty degree angle
it's the end jason this right over here is

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adjacent it's right next to it

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it's not my pot news

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it's the adjacent over the high positive so
it's too

00:09:06.790 --> 00:09:08.779
square roots of three

00:09:08.779 --> 00:09:10.320
and jay sent

00:09:10.320 --> 00:09:11.300
over

00:09:11.300 --> 00:09:13.820
over that partners over four

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or if we simplify that we divide the new renowned
abide to this the square root of three

00:09:19.290 --> 00:09:20.780
over too

00:09:20.780 --> 00:09:23.200
finally let's do that ended

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that tangent

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thirty degrees

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we go back to soak up

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draw

00:09:30.080 --> 00:09:34.900
so cut off poet tells us what to do it entered
it's opposite over adjacent

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you go to the thirty degree angle to the so
we care about ten to twelve thirty

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tended of thirty opposite is too

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opposite is to and the adjacent is to squirts
of three it's right next to it it's adjacent

00:09:47.150 --> 00:09:47.830
to it

00:09:47.830 --> 00:09:49.430
and jason means next to

00:09:49.430 --> 00:09:51.720
so to square roots of three

00:09:51.720 --> 00:09:53.110
so this is equal to

00:09:53.110 --> 00:09:56.820
the tunes cancel out one over the square root
of three

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oregon multiplied the numerator denominator
by the square three

00:10:00.340 --> 00:10:01.740
so we have

00:10:01.740 --> 00:10:03.290
square root of three

00:10:03.290 --> 00:10:05.200
over square root of three

00:10:05.200 --> 00:10:09.600
and so this is going to be equal to the numerator
square the story and then the denominator

00:10:09.600 --> 00:10:14.900
right overhear is just going to be three so
thats we've rationalize a square two three

00:10:14.900 --> 00:10:15.890
over three

00:10:15.890 --> 00:10:16.720
fair enough

00:10:16.720 --> 00:10:20.500
welch is the same triangle figure out the
tree gracias for the sixty degrees

00:10:20.500 --> 00:10:23.200
century we've already brought it

00:10:23.200 --> 00:10:24.890
so what is

00:10:24.890 --> 00:10:30.580
what is in the sign of the sixty degrees and
interval for getting the hang of it now

00:10:30.580 --> 00:10:35.480
side is opposite over js insult from the sock
it all out for the sixty degree angle website

00:10:35.480 --> 00:10:36.760
is opposite

00:10:36.760 --> 00:10:42.920
what opens out into the two squares of three
so the opposite side is two squares history

00:10:42.920 --> 00:10:47.880
from the sixty degree angle d<u>j</u> course ties
observer had taught me a story confuse you

00:10:47.880 --> 00:10:54.420
so it's opposite over high pot and his sister
squirts of three over four force a high partners

00:10:54.420 --> 00:10:58.750
so it is in equal to the simplifies to square
root of three

00:10:58.750 --> 00:11:00.000
over too

00:11:00.000 --> 00:11:03.139
what is the the co-sign a sixty degrees

00:11:03.139 --> 00:11:05.580
co-sign of sixty degrees

00:11:05.580 --> 00:11:10.330
so remember so cut off co-sign is adjacent
over my pot news

00:11:10.330 --> 00:11:15.070
it jason's is the two sides right next to
sixty degree angle so it's too

00:11:15.070 --> 00:11:17.920
over the hype on news which is four

00:11:17.920 --> 00:11:19.900
so this is equal to

00:11:19.900 --> 00:11:20.860
one-half

00:11:20.860 --> 00:11:22.120
and then finally

00:11:22.120 --> 00:11:24.460
what is a bit engine

00:11:24.460 --> 00:11:26.000
what is the tangent

00:11:26.000 --> 00:11:27.830
of sixty degrees

00:11:27.830 --> 00:11:32.790
well tended so cut toa attended is opposite
over adjacent

00:11:32.790 --> 00:11:34.220
opposite the sixty degrees

00:11:34.220 --> 00:11:36.130
is to squirts of three

00:11:36.130 --> 00:11:37.940
to squirts of three

00:11:37.940 --> 00:11:39.570
and adjacent to that

00:11:39.570 --> 00:11:43.020
in j sent to that

00:11:43.020 --> 00:11:45.470
adjacent to sixty degrees is too so it's

00:11:45.470 --> 00:11:48.750
opposite over it isn't too squirts of three
over too

00:11:48.750 --> 00:11:52.630
which is just equal to the square read of

00:11:52.630 --> 00:11:56.000
and i just wanted you look at these are related
to sign a third agrees is the same things

00:11:56.000 --> 00:11:58.150
of course i love sixty degrees

00:11:58.150 --> 00:12:01.750
because i'm a third agrees with the same thing
as a sign of sixty degrees and that these

00:12:01.750 --> 00:12:04.980
guys are the inverse of each other i think
if you think of a little bit about the strike

00:12:04.980 --> 00:12:05.440
both

00:12:05.440 --> 00:12:09.519
will start to make sense why will keep extending
this may be a lot more practice in the next

00:12:09.519 --> 00:12:10.110
few videos