0:00:00.859,0:00:05.370
buses to attack on a more examples of so we[br]make sure that we're getting district functioned
0:00:05.370,0:00:07.020
being down well
0:00:07.020,0:00:11.109
thoughts construct ourselves uh... some or[br]write triangles
0:00:11.109,0:00:15.299
let's construct ourselves some right right[br]as i want to be very clear the way up to find
0:00:15.299,0:00:19.829
it so far this all the work in right triangle[br]so if you try to find
0:00:19.829,0:00:20.579
treat
0:00:20.579,0:00:25.189
functions of angles that are part of right[br]rebels were to see a realtor construct right
0:00:25.189,0:00:28.079
rankles delicious focus on the right triangles[br]for now
0:00:28.079,0:00:33.470
so let's say that i have a triangle where[br]let's say this lengthy down here is seven
0:00:33.470,0:00:39.190
and let's say the length of the decide appear[br]let's say that that is four
0:00:39.190,0:00:43.170
let's figure out what the hyde park new silver[br]here is going to be so we know
0:00:43.170,0:00:45.350
please call the high partners
0:00:45.350,0:00:52.350
we know that age squared is going to be equal[br]to seven squared plus four squared we know
0:00:52.450,0:00:55.110
that from of the protagonist a room
0:00:55.110,0:00:57.190
that the hype on this where it is equal to
0:00:57.190,0:01:00.289
the square of each of the the some of the[br]squares
0:01:00.289,0:01:04.370
of the other two sides eight square zero seven[br]squared plus four squared
0:01:04.370,0:01:08.670
so this is the equal to forty-nine
0:01:08.670,0:01:09.729
sixteen
0:01:09.729,0:01:11.740
wordy nine plus sixteen
0:01:11.740,0:01:17.220
c forty nine plus ten is fifty-nine plus the[br]six is
0:01:17.220,0:01:21.979
sixty-five it is a sixty five so this age[br]squared
0:01:21.979,0:01:23.909
right each squared
0:01:23.909,0:01:28.310
it's different shade of plo_'s with eight[br]squared is equal to
0:01:28.310,0:01:32.480
sixty-five into that right forty nine point[br]status fifty nine plus another six
0:01:32.480,0:01:36.540
is the sixty-five or we could see that age[br]is equal to three take the square root of
0:01:36.540,0:01:38.120
both sides
0:01:38.120,0:01:39.340
square root
0:01:39.340,0:01:42.850
square root of sixty five and really can simplify[br]this at all
0:01:42.850,0:01:44.350
this is thirteen
0:01:44.350,0:01:48.710
this is the same thing is thirteen times five[br]both of those are not perfect squares and
0:01:48.710,0:01:49.619
they're both
0:01:49.619,0:01:51.860
prior to ten simplifydigital
0:01:51.860,0:01:55.750
so this is equal to the square root of sixty-five
0:01:55.750,0:01:57.710
ellis five the trade
0:01:57.710,0:02:04.710
let's find the trick functions for this angle[br]appear let's call that angle up there
0:02:05.060,0:02:06.270
so whatever you do it
0:02:06.270,0:02:09.679
you always want to write out at least for[br]me it works out to write down
0:02:09.679,0:02:11.219
soul cut off
0:02:11.219,0:02:12.829
so
0:02:12.829,0:02:16.429
so karto i have these big memories
0:02:16.429,0:02:17.919
of my
0:02:17.919,0:02:21.029
trigonometry teacher will be a rated in some[br]book i don't know who you know some about
0:02:21.029,0:02:25.159
some type of indian princess named so cut[br]or whatever but it's a very useful
0:02:25.159,0:02:28.079
new monica so we can apply so for those fine
0:02:28.079,0:02:34.099
let's say we want to find and uh... co-signed[br]we want to find the co-signed of our angle
0:02:34.099,0:02:37.779
we wanna find the close i never angle you[br]say so cut off
0:02:37.779,0:02:41.219
so the cop cod tells us what to do with cosign
0:02:41.219,0:02:43.070
the cop part tells us
0:02:43.070,0:02:46.930
that co-sign isn't jason over had gotten is
0:02:46.930,0:02:49.979
co-sign is equal to and jay sent
0:02:49.979,0:02:51.529
over-hyped ought to do is
0:02:51.529,0:02:55.909
so it's over here look over here to tell you[br]know what side is ed jason
0:02:55.909,0:02:57.759
well we know that the high partners
0:02:57.759,0:03:00.639
we know that i produce is this side over here
0:03:00.639,0:03:04.579
so it can't be that side they are all the[br]other side that's kind of adjacent to it that
0:03:04.579,0:03:06.949
given dot blot miss is this for
0:03:06.949,0:03:10.479
so the adjacent side over here that side is
0:03:10.479,0:03:14.149
three right next to the angle it's one of[br]the size of kind of forms the angle
0:03:14.149,0:03:15.269
it's for
0:03:15.269,0:03:16.669
over the hard part news
0:03:16.669,0:03:21.929
by partners we are do you know is square root[br]of sixty-five cents for
0:03:21.929,0:03:22.470
over
0:03:22.470,0:03:25.130
the square root uh... sixty-five
0:03:25.130,0:03:29.460
and sometimes people want you to rationalize[br]the denominator which means they don't like
0:03:29.460,0:03:34.049
to have an irrational number in denominator[br]like this where the sixty five
0:03:34.049,0:03:37.559
and if they if you wanna rewrite this without[br]the
0:03:37.559,0:03:41.179
irrational number in the nominate or you can[br]multiply the numerator and the denominator
0:03:41.179,0:03:43.049
by squares sixty-five
0:03:43.049,0:03:47.409
this clearly will not change the number cover[br]multiplying it by something over its elsewhere
0:03:47.409,0:03:51.279
multiplying the number by one that won't change[br]the number but at least in gets rid of the
0:03:51.279,0:03:54.539
irrational number that i meters of the numerator[br]becomes
0:03:54.539,0:03:57.749
four times of the square root of sixty-five
0:03:57.749,0:04:03.280
and denominator square two sixty five times[br]square to sixty-five is just going to be sixty-five
0:04:03.280,0:04:07.129
we did get rid of the rational number is still[br]there but is now in the numerator
0:04:07.129,0:04:09.629
now let's do the other trick functions
0:04:09.629,0:04:13.219
carelessly said the court rick functions will[br]learn in the future that there's a few tumble
0:04:13.219,0:04:15.249
but they're all derived from these
0:04:15.249,0:04:19.889
fussing about the sign of state is once again[br]to go to so cut off
0:04:19.889,0:04:25.650
the sole tells what to do it signed side of[br]the opposite over high positives
0:04:25.650,0:04:26.300
sign
0:04:26.300,0:04:27.629
is equal to
0:04:27.629,0:04:31.509
opposite over hypothesize opposite over high[br]partners
0:04:31.509,0:04:34.040
so for this and all tried as officer
0:04:34.040,0:04:35.129
we just go
0:04:35.129,0:04:38.930
opposite itworld opens into it's opposite[br]the seven
0:04:38.930,0:04:41.909
so the opposite side is the seven this is
0:04:41.909,0:04:44.349
right here that is the opposite side
0:04:44.349,0:04:45.710
and then in the
0:04:45.710,0:04:51.039
hypothalamus opposite overabundance of hypothesis[br]in the square root of sixty-five
0:04:51.039,0:04:52.760
square root sixty-five
0:04:52.760,0:04:57.989
and once again if we want to rationalize this[br]week a multiply times square in sixty five
0:04:57.989,0:05:00.469
over the square to sixty-five
0:05:00.469,0:05:06.500
numerator will get seven square roots of sixty-five[br]and in the denominator we will get jest
0:05:06.500,0:05:08.089
sixty-five again
0:05:08.089,0:05:10.219
knowledge do tangent
0:05:10.219,0:05:12.479
let us do ten gente
0:05:12.479,0:05:15.689
so if i ask you the tangent
0:05:15.689,0:05:17.330
but ended up there
0:05:17.330,0:05:19.979
once again go back to soak up
0:05:19.979,0:05:23.120
toa the toll apart tells us what to do a tangent
0:05:23.120,0:05:24.550
it tells us
0:05:24.550,0:05:27.319
it tells us that tangent
0:05:27.319,0:05:31.989
is equal to opposite over adjacent is equal[br]to opposite
0:05:31.989,0:05:33.379
over
0:05:33.379,0:05:35.639
opposite over ed to use it
0:05:35.639,0:05:36.970
so for this and all
0:05:36.970,0:05:41.380
what is opposite we've already figured it[br]out it's evident opens into the seventh opposite
0:05:41.380,0:05:42.549
the seven
0:05:42.549,0:05:44.409
so it's seven
0:05:44.409,0:05:46.089
over website is adjacent
0:05:46.089,0:05:48.009
well this for is adjacent
0:05:48.009,0:05:51.040
this for is adjacent to the jason side is[br]four
0:05:51.040,0:05:52.639
so it's seven
0:05:52.639,0:05:54.049
over
0:05:54.049,0:05:54.950
and were dot
0:05:54.950,0:05:59.349
we figured out all of the trade ratios for[br]baidoa let's do it other one
0:05:59.349,0:06:03.129
let's do another one on the colluded concrete[br]'cause right now we've been saying oh was
0:06:03.129,0:06:06.879
tentative actress tens of their lives make[br]a little bit more concrete
0:06:06.879,0:06:08.310
let's say
0:06:08.310,0:06:11.059
let's say i mean drawn other right triangle
0:06:11.059,0:06:13.999
list another right triangle here
0:06:13.999,0:06:15.250
everything we're dealing with
0:06:15.250,0:06:18.110
these are going to be right triangles
0:06:18.110,0:06:19.650
let's say the high partners
0:06:19.650,0:06:21.919
has the length
0:06:21.919,0:06:24.440
let's say that the side over here
0:06:24.440,0:06:26.469
has length too
0:06:26.469,0:06:31.830
and let's say that this length overhears will[br]be to times the square root of three we can
0:06:31.830,0:06:33.559
verify that this works
0:06:33.559,0:06:38.279
if you have this aside squared so yet let[br]me write down two times the square root of
0:06:38.279,0:06:40.039
three squared
0:06:40.039,0:06:42.930
plus to squared is equal to what
0:06:42.930,0:06:43.889
this is
0:06:43.889,0:06:47.119
to there's going to be four times three
0:06:47.119,0:06:49.549
four times three plus four
0:06:49.549,0:06:54.619
and this is going to be equal to twelve plus[br]for the for the sixteen and sixteen is indeed
0:06:54.619,0:06:57.729
four square so this does he call for squared
0:06:57.729,0:07:02.419
it does equal foursquare it satisfies the[br]protagonist hero
0:07:02.419,0:07:06.529
if you remember some of your work from thirty[br]sixty ninety triangles that you might have
0:07:06.529,0:07:09.050
learned in geometry you might recognize that[br]this
0:07:09.050,0:07:13.030
is eight thirty sixty ninety triangle this[br]right here is our right angle i should have
0:07:13.030,0:07:16.219
drawn it from the get go to show that this[br]is the right triangle
0:07:16.219,0:07:20.210
this angle right over here is our thirty degree[br]angle
0:07:20.210,0:07:24.430
and then disable appear the single appears[br]is
0:07:24.430,0:07:26.019
sixty degree angle
0:07:26.019,0:07:28.139
and it's a pretty sixteen ninety because
0:07:28.139,0:07:31.990
the side opposite the thirty degrees is half[br]of my partners
0:07:31.990,0:07:36.650
and in the side opposite the sixty degrees[br]is a square to three times the other side
0:07:36.650,0:07:38.280
that's not the hype on this
0:07:38.280,0:07:41.910
so that's that we're not gonna the student[br]was peer review of thirty sixty ninety triangles
0:07:41.910,0:07:43.110
although i just get it
0:07:43.110,0:07:46.830
let's actually fifi and the trigger issues[br]for the different angles
0:07:46.830,0:07:48.080
so if i were to ask you
0:07:48.080,0:07:51.059
or if anyone would ask you what is
0:07:51.059,0:07:54.389
what is the signed of thirty degrees
0:07:54.389,0:07:58.520
and remember thirty degrees is one of the[br]eagles in this triangle but it would apply
0:07:58.520,0:08:01.520
whenever you have a thirty degree angle and[br]you're dealing with the right rangel will
0:08:01.520,0:08:04.970
have broader definitions of the future but[br]if you see a sign of thirty degrees
0:08:04.970,0:08:10.099
hey this ain't gold right over here is thirty[br]degrees so i can use this right triangle
0:08:10.099,0:08:12.849
and we should remember so catawba
0:08:12.849,0:08:14.439
rewrite it so
0:08:14.439,0:08:15.949
ka
0:08:15.949,0:08:17.270
toa
0:08:17.270,0:08:22.159
sign tells us more also tells us what to do[br]it signed side is opposite over hype rotten
0:08:22.159,0:08:23.050
is
0:08:23.050,0:08:26.199
sign up thirty degrees is the opposite side
0:08:26.199,0:08:29.279
that is the opposite side which is to
0:08:29.279,0:08:32.149
over the hard part is the hype on this year's[br]for
0:08:32.149,0:08:35.800
it is to ford's which is the same thing as[br]one-half
0:08:35.800,0:08:39.020
five thirty degrees you'll see is always going[br]to be equal
0:08:39.020,0:08:40.760
to one-half
0:08:40.760,0:08:42.190
now what is
0:08:42.190,0:08:43.910
the duck cosign
0:08:43.910,0:08:45.980
what is the co-signed of
0:08:45.980,0:08:47.160
thirty degrees
0:08:47.160,0:08:49.969
once again go back to seoul cut off
0:08:49.969,0:08:56.070
the cod tells us what to do with co-sign co-sign[br]isn't jay sent over high popped in his
0:08:56.070,0:08:59.940
so for looking at the thirty degree angle[br]it's the end jason this right over here is
0:08:59.940,0:09:01.639
adjacent it's right next to it
0:09:01.639,0:09:02.960
it's not my pot news
0:09:02.960,0:09:06.790
it's the adjacent over the high positive so[br]it's too
0:09:06.790,0:09:08.779
square roots of three
0:09:08.779,0:09:10.320
and jay sent
0:09:10.320,0:09:11.300
over
0:09:11.300,0:09:13.820
over that partners over four
0:09:13.820,0:09:19.290
or if we simplify that we divide the new renowned[br]abide to this the square root of three
0:09:19.290,0:09:20.780
over too
0:09:20.780,0:09:23.200
finally let's do that ended
0:09:23.200,0:09:25.880
that tangent
0:09:25.880,0:09:27.850
thirty degrees
0:09:27.850,0:09:29.179
we go back to soak up
0:09:29.179,0:09:30.080
draw
0:09:30.080,0:09:34.900
so cut off poet tells us what to do it entered[br]it's opposite over adjacent
0:09:34.900,0:09:38.860
you go to the thirty degree angle to the so[br]we care about ten to twelve thirty
0:09:38.860,0:09:42.760
tended of thirty opposite is too
0:09:42.760,0:09:47.150
opposite is to and the adjacent is to squirts[br]of three it's right next to it it's adjacent
0:09:47.150,0:09:47.830
to it
0:09:47.830,0:09:49.430
and jason means next to
0:09:49.430,0:09:51.720
so to square roots of three
0:09:51.720,0:09:53.110
so this is equal to
0:09:53.110,0:09:56.820
the tunes cancel out one over the square root[br]of three
0:09:56.820,0:10:00.340
oregon multiplied the numerator denominator[br]by the square three
0:10:00.340,0:10:01.740
so we have
0:10:01.740,0:10:03.290
square root of three
0:10:03.290,0:10:05.200
over square root of three
0:10:05.200,0:10:09.600
and so this is going to be equal to the numerator[br]square the story and then the denominator
0:10:09.600,0:10:14.900
right overhear is just going to be three so[br]thats we've rationalize a square two three
0:10:14.900,0:10:15.890
over three
0:10:15.890,0:10:16.720
fair enough
0:10:16.720,0:10:20.500
welch is the same triangle figure out the[br]tree gracias for the sixty degrees
0:10:20.500,0:10:23.200
century we've already brought it
0:10:23.200,0:10:24.890
so what is
0:10:24.890,0:10:30.580
what is in the sign of the sixty degrees and[br]interval for getting the hang of it now
0:10:30.580,0:10:35.480
side is opposite over js insult from the sock[br]it all out for the sixty degree angle website
0:10:35.480,0:10:36.760
is opposite
0:10:36.760,0:10:42.920
what opens out into the two squares of three[br]so the opposite side is two squares history
0:10:42.920,0:10:47.880
from the sixty degree angle dj course ties[br]observer had taught me a story confuse you
0:10:47.880,0:10:54.420
so it's opposite over high pot and his sister[br]squirts of three over four force a high partners
0:10:54.420,0:10:58.750
so it is in equal to the simplifies to square[br]root of three
0:10:58.750,0:11:00.000
over too
0:11:00.000,0:11:03.139
what is the the co-sign a sixty degrees
0:11:03.139,0:11:05.580
co-sign of sixty degrees
0:11:05.580,0:11:10.330
so remember so cut off co-sign is adjacent[br]over my pot news
0:11:10.330,0:11:15.070
it jason's is the two sides right next to[br]sixty degree angle so it's too
0:11:15.070,0:11:17.920
over the hype on news which is four
0:11:17.920,0:11:19.900
so this is equal to
0:11:19.900,0:11:20.860
one-half
0:11:20.860,0:11:22.120
and then finally
0:11:22.120,0:11:24.460
what is a bit engine
0:11:24.460,0:11:26.000
what is the tangent
0:11:26.000,0:11:27.830
of sixty degrees
0:11:27.830,0:11:32.790
well tended so cut toa attended is opposite[br]over adjacent
0:11:32.790,0:11:34.220
opposite the sixty degrees
0:11:34.220,0:11:36.130
is to squirts of three
0:11:36.130,0:11:37.940
to squirts of three
0:11:37.940,0:11:39.570
and adjacent to that
0:11:39.570,0:11:43.020
in j sent to that
0:11:43.020,0:11:45.470
adjacent to sixty degrees is too so it's
0:11:45.470,0:11:48.750
opposite over it isn't too squirts of three[br]over too
0:11:48.750,0:11:52.630
which is just equal to the square read of
0:11:52.630,0:11:56.000
and i just wanted you look at these are related[br]to sign a third agrees is the same things
0:11:56.000,0:11:58.150
of course i love sixty degrees
0:11:58.150,0:12:01.750
because i'm a third agrees with the same thing[br]as a sign of sixty degrees and that these
0:12:01.750,0:12:04.980
guys are the inverse of each other i think[br]if you think of a little bit about the strike
0:12:04.980,0:12:05.440
both
0:12:05.440,0:12:09.519
will start to make sense why will keep extending[br]this may be a lot more practice in the next
0:12:09.519,0:12:10.110
few videos