Basic Trigonometry II

One of the most popular Khan Academy videos, Basic Trigonometry doesn't have any subtitles - help translate it into as many languages possible!

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