buses to attack on a more examples of so we make sure that we're getting district functioned
being down well
thoughts construct ourselves uh... some or write triangles
let's construct ourselves some right right as i want to be very clear the way up to find
it so far this all the work in right triangle so if you try to find
treat
functions of angles that are part of right rebels were to see a realtor construct right
rankles delicious focus on the right triangles for now
so let's say that i have a triangle where let's say this lengthy down here is seven
and let's say the length of the decide appear let's say that that is four
let's figure out what the hyde park new silver here is going to be so we know
please call the high partners
we know that age squared is going to be equal to seven squared plus four squared we know
that from of the protagonist a room
that the hype on this where it is equal to
the square of each of the the some of the squares
of the other two sides eight square zero seven squared plus four squared
so this is the equal to forty-nine
sixteen
wordy nine plus sixteen
c forty nine plus ten is fifty-nine plus the six is
sixty-five it is a sixty five so this age squared
right each squared
it's different shade of plo_'s with eight squared is equal to
sixty-five into that right forty nine point status fifty nine plus another six
is the sixty-five or we could see that age is equal to three take the square root of
both sides
square root
square root of sixty five and really can simplify this at all
this is thirteen
this is the same thing is thirteen times five both of those are not perfect squares and
they're both
prior to ten simplifydigital
so this is equal to the square root of sixty-five
ellis five the trade
let's find the trick functions for this angle appear let's call that angle up there
so whatever you do it
you always want to write out at least for me it works out to write down
soul cut off
so
so karto i have these big memories
of my
trigonometry teacher will be a rated in some book i don't know who you know some about
some type of indian princess named so cut or whatever but it's a very useful
new monica so we can apply so for those fine
let's say we want to find and uh... co-signed we want to find the co-signed of our angle
we wanna find the close i never angle you say so cut off
so the cop cod tells us what to do with cosign
the cop part tells us
that co-sign isn't jason over had gotten is
co-sign is equal to and jay sent
over-hyped ought to do is
so it's over here look over here to tell you know what side is ed jason
well we know that the high partners
we know that i produce is this side over here
so it can't be that side they are all the other side that's kind of adjacent to it that
given dot blot miss is this for
so the adjacent side over here that side is
three right next to the angle it's one of the size of kind of forms the angle
it's for
over the hard part news
by partners we are do you know is square root of sixty-five cents for
over
the square root uh... sixty-five
and sometimes people want you to rationalize the denominator which means they don't like
to have an irrational number in denominator like this where the sixty five
and if they if you wanna rewrite this without the
irrational number in the nominate or you can multiply the numerator and the denominator
by squares sixty-five
this clearly will not change the number cover multiplying it by something over its elsewhere
multiplying the number by one that won't change the number but at least in gets rid of the
irrational number that i meters of the numerator becomes
four times of the square root of sixty-five
and denominator square two sixty five times square to sixty-five is just going to be sixty-five
we did get rid of the rational number is still there but is now in the numerator
now let's do the other trick functions
carelessly said the court rick functions will learn in the future that there's a few tumble
but they're all derived from these
fussing about the sign of state is once again to go to so cut off
the sole tells what to do it signed side of the opposite over high positives
sign
is equal to
opposite over hypothesize opposite over high partners
so for this and all tried as officer
we just go
opposite itworld opens into it's opposite the seven
so the opposite side is the seven this is
right here that is the opposite side
and then in the
hypothalamus opposite overabundance of hypothesis in the square root of sixty-five
square root sixty-five
and once again if we want to rationalize this week a multiply times square in sixty five
over the square to sixty-five
numerator will get seven square roots of sixty-five and in the denominator we will get jest
sixty-five again
knowledge do tangent
let us do ten gente
so if i ask you the tangent
but ended up there
once again go back to soak up
toa the toll apart tells us what to do a tangent
it tells us
it tells us that tangent
is equal to opposite over adjacent is equal to opposite
over
opposite over ed to use it
so for this and all
what is opposite we've already figured it out it's evident opens into the seventh opposite
the seven
so it's seven
over website is adjacent
well this for is adjacent
this for is adjacent to the jason side is four
so it's seven
over
and were dot
we figured out all of the trade ratios for baidoa let's do it other one
let's do another one on the colluded concrete 'cause right now we've been saying oh was
tentative actress tens of their lives make a little bit more concrete
let's say
let's say i mean drawn other right triangle
list another right triangle here
everything we're dealing with
these are going to be right triangles
let's say the high partners
has the length
let's say that the side over here
has length too
and let's say that this length overhears will be to times the square root of three we can
verify that this works
if you have this aside squared so yet let me write down two times the square root of
three squared
plus to squared is equal to what
this is
to there's going to be four times three
four times three plus four
and this is going to be equal to twelve plus for the for the sixteen and sixteen is indeed
four square so this does he call for squared
it does equal foursquare it satisfies the protagonist hero
if you remember some of your work from thirty sixty ninety triangles that you might have
learned in geometry you might recognize that this
is eight thirty sixty ninety triangle this right here is our right angle i should have
drawn it from the get go to show that this is the right triangle
this angle right over here is our thirty degree angle
and then disable appear the single appears is
sixty degree angle
and it's a pretty sixteen ninety because
the side opposite the thirty degrees is half of my partners
and in the side opposite the sixty degrees is a square to three times the other side
that's not the hype on this
so that's that we're not gonna the student was peer review of thirty sixty ninety triangles
although i just get it
let's actually fifi and the trigger issues for the different angles
so if i were to ask you
or if anyone would ask you what is
what is the signed of thirty degrees
and remember thirty degrees is one of the eagles in this triangle but it would apply
whenever you have a thirty degree angle and you're dealing with the right rangel will
have broader definitions of the future but if you see a sign of thirty degrees
hey this ain't gold right over here is thirty degrees so i can use this right triangle
and we should remember so catawba
rewrite it so
ka
toa
sign tells us more also tells us what to do it signed side is opposite over hype rotten
is
sign up thirty degrees is the opposite side
that is the opposite side which is to
over the hard part is the hype on this year's for
it is to ford's which is the same thing as one-half
five thirty degrees you'll see is always going to be equal
to one-half
now what is
the duck cosign
what is the co-signed of
thirty degrees
once again go back to seoul cut off
the cod tells us what to do with co-sign co-sign isn't jay sent over high popped in his
so for looking at the thirty degree angle it's the end jason this right over here is
adjacent it's right next to it
it's not my pot news
it's the adjacent over the high positive so it's too
square roots of three
and jay sent
over
over that partners over four
or if we simplify that we divide the new renowned abide to this the square root of three
over too
finally let's do that ended
that tangent
thirty degrees
we go back to soak up
draw
so cut off poet tells us what to do it entered it's opposite over adjacent
you go to the thirty degree angle to the so we care about ten to twelve thirty
tended of thirty opposite is too
opposite is to and the adjacent is to squirts of three it's right next to it it's adjacent
to it
and jason means next to
so to square roots of three
so this is equal to
the tunes cancel out one over the square root of three
oregon multiplied the numerator denominator by the square three
so we have
square root of three
over square root of three
and so this is going to be equal to the numerator square the story and then the denominator
right overhear is just going to be three so thats we've rationalize a square two three
over three
fair enough
welch is the same triangle figure out the tree gracias for the sixty degrees
century we've already brought it
so what is
what is in the sign of the sixty degrees and interval for getting the hang of it now
side is opposite over js insult from the sock it all out for the sixty degree angle website
is opposite
what opens out into the two squares of three so the opposite side is two squares history
from the sixty degree angle dj course ties observer had taught me a story confuse you
so it's opposite over high pot and his sister squirts of three over four force a high partners
so it is in equal to the simplifies to square root of three
over too
what is the the co-sign a sixty degrees
co-sign of sixty degrees
so remember so cut off co-sign is adjacent over my pot news
it jason's is the two sides right next to sixty degree angle so it's too
over the hype on news which is four
so this is equal to
one-half
and then finally
what is a bit engine
what is the tangent
of sixty degrees
well tended so cut toa attended is opposite over adjacent
opposite the sixty degrees
is to squirts of three
to squirts of three
and adjacent to that
in j sent to that
adjacent to sixty degrees is too so it's
opposite over it isn't too squirts of three over too
which is just equal to the square read of
and i just wanted you look at these are related to sign a third agrees is the same things
of course i love sixty degrees
because i'm a third agrees with the same thing as a sign of sixty degrees and that these
guys are the inverse of each other i think if you think of a little bit about the strike
both
will start to make sense why will keep extending this may be a lot more practice in the next
few videos