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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 right
as i want to be very clear the way up to find
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it so far this all the work in right triangle
so if you try to find
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treat
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functions of angles that are part of right
rebels were to see a realtor construct right
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rankles delicious 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 the decide appear
let's say that that is four
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let's figure out what the hyde park new silver
here is going to be so we know
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please call the high partners
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we know that age squared is going to be equal
to seven squared plus four squared we know
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that from of the protagonist a room
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that the hype on this where it is equal to
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the square of each of the the some of the
squares
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of the other two sides eight square zero seven
squared plus four squared
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so this is the equal to forty-nine
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sixteen
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wordy nine plus sixteen
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c forty nine plus ten is fifty-nine plus the
six is
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sixty-five it is a sixty five so this age
squared
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right each squared
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it's different shade of plo_'s with eight
squared is equal to
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sixty-five into that right forty nine point
status fifty nine plus another six
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is the sixty-five or we could see that age
is equal to three 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 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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prior to ten simplifydigital
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so this is equal to the square root of sixty-five
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ellis five the trade
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let's find the trick functions for this angle
appear let's call that angle up there
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so whatever you do it
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you always want to write out at least for
me it works out to write down
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soul cut off
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so
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so karto i have these big memories
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of my
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trigonometry teacher will be a rated in some
book i don't know who you know some about
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some type of indian princess named so cut
or whatever but it's a very useful
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new monica so we can apply so for those fine
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let's say we want to find and uh... co-signed
we want to find the co-signed of our angle
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we wanna find the close i never angle you
say so cut off
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so the cop cod tells us what to do with cosign
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the cop part tells us
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that co-sign isn't jason over had gotten is
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co-sign is equal to and jay sent
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over-hyped ought to do is
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so it's over here look over here to tell you
know what side is ed jason
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well we know that the high partners
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we know that i produce is this side over here
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so it can't be that side they are all the
other side that's kind of adjacent to it that
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given dot blot miss is this for
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so the adjacent side over here that side is
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three right next to the angle it's one of
the size of kind of forms the angle
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it's for
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over the hard part news
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by partners we are do you know is square root
of sixty-five cents for
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over
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the square root uh... sixty-five
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and sometimes people want you to rationalize
the denominator which means they don't like
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to have an irrational number in denominator
like this where the sixty five
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and if they if you wanna rewrite this without
the
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irrational number in the nominate or you can
multiply the numerator and the denominator
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by squares sixty-five
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this clearly will not change the number cover
multiplying it by something over its elsewhere
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multiplying the number by one that won't change
the number but at least in gets rid of the
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irrational number that i meters of the numerator
becomes
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four times of 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 did get rid of the rational number is still
there but is 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
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square roots of three
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and jay sent
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over
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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
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over too
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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
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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
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to it
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and jason means next to
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so to square roots of three
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so this is equal to
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the tunes cancel out one over the square root
of three
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oregon multiplied the numerator denominator
by the square three
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so we have
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square root of three
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over square root of three
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and so this is going to be equal to the numerator
square the story and then the denominator
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right overhear is just going to be three so
thats we've rationalize a square two three
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over three
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fair enough
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welch is the same triangle figure out the
tree gracias for the sixty degrees
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century we've already brought it
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so what is
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what is in the sign of the sixty degrees and
interval for getting the hang of it now
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side is opposite over js insult from the sock
it all out for the sixty degree angle website
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is opposite
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what opens out into the two squares of three
so the opposite side is two squares history
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from the sixty degree angle dj course ties
observer had taught me a story confuse you
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so it's opposite over high pot and his sister
squirts of three over four force a high partners
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so it is in equal to the simplifies to square
root of three
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over too
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what is the the co-sign a sixty degrees
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co-sign of sixty degrees
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so remember so cut off co-sign is adjacent
over my pot news
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it jason's is the two sides right next to
sixty degree angle so it's too
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over the hype on news which is four
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so this is equal to
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one-half
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and then finally
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what is a bit engine
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what is the tangent
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of sixty degrees
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well tended so cut toa attended is opposite
over adjacent
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opposite the sixty degrees
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is to squirts of three
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to squirts of three
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and adjacent to that
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in j sent to that
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adjacent to sixty degrees is too so it's
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opposite over it isn't too squirts of three
over too
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which is just equal to the square read of
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and i just wanted you look at these are related
to sign a third agrees is the same things
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of course i love sixty degrees
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because i'm a third agrees with the same thing
as a sign of sixty degrees and that these
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guys are the inverse of each other i think
if you think of a little bit about the strike
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both
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will start to make sense why will keep extending
this may be a lot more practice in the next
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few videos