Trigonometry made easy - Free Educational videos for Students in K-12

Trigonometry made easy - By tecmath

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00:00	get a welcome to Tech Math channel . What we're
00:02	going to be having a look at in this video
00:04	is trigonometry . So sit back and learn all about
00:06	it and if you like the video , please remember
00:08	hit the like button beneath the video there and subscribe
00:11	to the Tech mouth channel . So trigonometry deals with
00:14	this particular shape here , a right angle triangle .
00:17	And what it does is it's a branch of mathematics
00:20	that studies the relationships between the science of this triangle
00:23	and the angles that occur within it . Okay ,
00:26	so pretty much we can use say an angle here
00:30	and a side length to work out other side leaks
00:33	. Or we could use tattoo side legs here to
00:35	work out unknown angles . That's what trigonometry allows us
00:38	to do . So how does it do this ?
00:40	Well , it's fairly simple if we want to consider
00:43	, say an angle here in this triangle . So
00:46	I'm just going to put this down and this angle
00:47	here is called feta . Pretty much what it's saying
00:50	is this for this particular angle here , in a
00:53	right angle triangle , in this particular location , In
00:56	that right angle triangle . These two side links here
00:59	would have a particular ratio . They would always be
01:02	an equivalent length compared to one another . Okay ,
01:05	this length and this length would have a certain ratio
01:07	of this length and this length would have a certain
01:09	ratio . And trigonometry uses this to be able to
01:12	work out unknown side lengths and unknown angles . So
01:17	how do we do this ? Well , the first
01:18	thing we have to do is we have to be
01:20	able to label the sides of this particular triangle .
01:24	So in this particular triangle , you notice we've got
01:26	a right angle here , we have this angle feta
01:28	, which we are we've already labeled here . We
01:31	also have three sides here , we have this longest
01:34	side here . The longest side is called the high
01:37	pot news . I'm going to write that in the
01:38	high pot and news . I'm going to put that
01:42	down as a high church here we have the opposite
01:46	side . Alright that over here . The opposite .
01:50	What I mean by that this particular side is opposite
01:53	feet up . We put that down as a no
01:56	along this particular side , this remaining side which is
01:59	next to feeder . We have the adjacent adjacent adjacent
02:04	means next to . And we label that with an
02:07	A . So now we've done that as I would
02:10	say all these sidelines here , the opposite the adjacent
02:13	to high point news . All have particular ratios to
02:17	one another based on whatever this particular angle here is
02:21	. Okay , so there's three different functions we are
02:24	thinking about when we're thinking about these ratios because we
02:26	have three different ways . We can compare the sides
02:28	. We can be comparing these two sides to feed
02:30	her or these two sides . We can be comparing
02:33	these two sides and our three main trigger gnomic functions
02:37	are as follows . We have the sine function which
02:40	is the ratio of the opposite and the high point
02:43	news . We have the cosine function which is the
02:47	ratio between the adjacent and the high pot news .
02:51	And we have the tangent function which is the ratio
02:55	between the opposite and the adjacent function . Now there's
03:00	a really really easy way we can remember these when
03:03	we're doing these and this is as follows . Alright
03:05	this pneumonic down right now and here it is .
03:08	Some old hags can't always hack their old age .
03:12	Okay . Shh . Sine equals opposite over . Hypotenuse
03:17	can't always hack cause eagles adjacent . Over . Hypotenuse
03:20	, their old age tan equals opposite over adjacent .
03:24	So when I was solving a trigger gnomic equation ,
03:27	pretty much the very first thing I do is what
03:30	we did . First off here , I'd label these
03:31	unknown sides . The next thing I do is I
03:34	determine which trigger gnomic function I was going to use
03:38	. So we're pretty much all set now to solve
03:40	some true economic problems . So let's do that .
03:43	So for our first example here we have a right
03:45	angle triangle . Okay it has an angle of 35°.
03:49	. It has one side length of 12 m and
03:52	another unknown side length which we're gonna be trying to
03:55	work out . So the very first step to work
03:57	out this unknown side leaf is we are going to
03:59	do what we do with any true economic equation or
04:02	any true economic problem . We are going to label
04:04	the unknown sides . So first off we have this
04:07	long side here which is the high pot news .
04:11	Then we have this side which is opposite . This
04:13	angle , opposite is 35 here . This is the
04:16	opposite . So which of our true economic functions deals
04:19	with the opposite and the high pot news . And
04:21	you're gonna say that it's sign here sign is equal
04:24	to opposite overhyped news . Some old hags . So
04:27	I'm gonna write this down sign feta is equal to
04:31	the opposite over there . Hi pot news . And
04:35	now what we do is we just go through and
04:37	substitute in our values has signed feeder . This is
04:40	signed 35° is equal to the opposite . The opposite
04:46	is what we're trying to work out here . X
04:48	. So I put that in his ex Over the
04:50	high pot news which is 12 . So we can
04:55	now work this out a little bit further . We
04:57	could actually say , Okay , uh signed 35 .
05:00	We put that into a calculator . We're going to
05:02	get the answer is 0.57 which is equal to X
05:07	over 12 . What can we do now ? So
05:11	what we have to do is we have to get
05:12	X by itself . Okay , So X is going
05:16	to be equal to what there's a little trick I
05:18	use here . This may or may not help .
05:20	You may or may not like it . Okay .
05:22	I'm sure I'm gonna get plenty of hate for this
05:24	. But what I do is this when I'm not
05:26	certain what to do here and I'm trying to solve
05:28	this particular problem here , I just write up an
05:30	equation next to it . A friendly equation as it
05:33	were the equation I'm going to write as this one
05:35	, three equal 6/2 . And we're trying to deal
05:39	with this particular value here , The value up here
05:43	. So what would you do with three and two
05:45	to get six ? We would multiply them . So
05:47	we're going to multiply These two numbers 12 Times 0.57
05:53	, so 12 times 0.57 . And we'll get our
05:57	answer . So if you do that , what answer
05:59	do you get you get our answer of 6.88 m
06:04	. Okay , so this side link , this opposite
06:07	is 6.88 m and that's how easy trigonometry is to
06:10	use . Okay , so we're gonna go through another
06:13	example and then I'm going to go through an example
06:15	where I look at how to work out the angle
06:17	from 29 side things . So it's a bit of
06:20	a tweak here , so stay tuned for that one
06:22	as well . Okay , but let's just go through
06:24	another one of these time examples . Okay , for
06:26	our second example , let's have a look . We
06:28	have a right angle triangle . We have an angle
06:30	of 48°. . We know that this side length here
06:33	is 15 and we're trying to work out this unknown
06:36	side length here . So let's label our sides first
06:40	. We have this particular site here which is opposite
06:44	the angle here . So that's the opposite . We
06:46	know that this one here is the high pollen .
06:48	Is that's the easy one spot . So it leaves
06:50	this one here being the adjacent . Okay , and
06:54	it makes sense . It's the shorter one that's running
06:56	next to the angle here . So which one of
06:58	these functions uses opposite and adjacent you're going to see
07:01	here is tan ted feta equals opposite over adjacent .
07:08	So let's sub in our values now . So tan
07:10	feeder becomes tan 48 degrees , Which is equal to
07:15	the opposite , which is 50 m Over Aaron .
07:20	No one x . Okay , we can put 1048
07:25	into the calculator . If you do this , you're
07:27	gonna get this answer of 1.11 . Okay . The
07:30	opposite and adjacent have that particular ratio of 1.11 for
07:34	an angle of 48° which is equal to 15 over
07:37	X . So now to solve for X and if
07:40	you're not certain what to do you might know this
07:42	straight away but you could do this once again you
07:44	can go OK three equals six divided by two .
07:48	And we're trying to work out the value on the
07:50	bottom here . The two . So that would be
07:51	six divided by three . This number divided by this
07:54	number , this number divided by this number X .
07:58	Xia is going to be equal to this number divided
08:01	by this number 15 divided by 1.11 . Which is
08:06	equal to how much 13.51 matters . Okay , so
08:13	that's how that particular type of our function in trigonometry
08:17	works . It's pretty simple right now , we're gonna
08:19	go through some examples . We're going to look at
08:21	how to work out the angle from snow inside links
08:24	. It's fairly simple . There's just a couple of
08:26	tweaks with this . So in this example here we
08:29	have a right angle triangle and we know to side
08:31	links . We know that this side length here is
08:33	100 and five m and we know that this side
08:35	length here is 33 m . What we're trying to
08:38	find out is we're trying to find out this unknown
08:40	angle that would accommodate these side links . So how
08:43	do we do that ? Well , it's just one
08:44	little variant and I'll get to that as we are
08:46	do this particular problem . The very start though is
08:49	exactly the same . We are just going to go
08:51	through a label whether our sides are opposite . High
08:54	pot news are adjacent . So we know this long
08:57	side here is going to be the high pot news
09:00	. We know that this side opposite angle feature here
09:04	is the opposite . So which one are the functions
09:07	that we're dealing with ? This is our second thing
09:09	we can deal with which function and we're going to
09:11	do dealing with sign here . Sign feta is going
09:16	to equal the opposite over the high pot news .
09:20	So what is the opposite over the high point news
09:24	? We're going to see here that we have The
09:27	opposite , which is 33 m over 105 m .
09:33	Okay , so signed feeder is equal to 33 over
09:37	105 . It would have worked this out . What's
09:39	33 divided by 105 . You're gonna see that sign
09:43	feeder is equal to 0.314 . Okay , that's just
09:49	a matter of going . 33 divided by 105 .
09:52	And we get this answer here . So what we
09:54	do now is just a little variant Because we have
09:58	to actually go back . We've got the ratio .
09:59	We're trying to go back to the angle . You're
10:01	going to notice some calculators . That is either a
10:04	second function or something like that . That allows you
10:07	to go from sign to this particular thing , sign
10:11	-1 . OK . We want to be using that
10:14	here . We're going to be hitting 30.314 and we're
10:17	gonna hit sign negative one or second function side .
10:21	Here we do that . We're going to get the
10:24	answer of feta being equal to 18.3°. . Okay ,
10:31	So just make sure you know how to do that
10:33	on your calculator . Okay , uh anyway , we'll
10:36	go through one more of these examples . Okay ,
10:39	for this example here we have a right angle triangle
10:42	. We have to sidelines . We know we know
10:44	that this one here is 17 . You know this
10:46	one here is 12 and we're trying to work out
10:48	the angle that accommodates these . So let's go through
10:51	and do this . The very first thing we do
10:53	is we're going to label our sides . We have
10:55	the hypotheses which you can see , we're not gonna
10:58	be dealing with the opposite . Were in fact dealing
11:00	with the adjacent . So which one of these functions
11:03	are we dealing with ? And you're going to see
11:05	here the adjacent to the high pot news is the
11:08	co signed function . So , cause feeder is equal
11:13	to the adjacent over the high pot news . Okay
11:18	, So what is that going to be ? Cause
11:20	feeder which is what we're trying to find out is
11:23	equal to the adjacent which is 12 over The High
11:28	Point News which is 17 . So we work out
11:30	what's well divided by 17 means we get the answer
11:34	of 0.71 Okay . Cause fever is equal to 0.71
11:41	So we're going to be not working out cause we're
11:43	gonna be working at the inverse of cause caused the
11:46	negative one . So you're gonna get second function Cause
11:49	and you're going to get when you do that .
11:51	You're going to get the answer for Feta Feta or
11:53	an angle here is equal to 45.1°. . So that's
11:59	how you go doing trigonometry . And its most basic
12:02	it's pretty simple right ? It's just those tweets there
12:05	and it's also getting to know the calculator that you
12:07	are using . So anyway , hopefully that video is
12:09	of some help to you . If you've got any
12:11	problems , please let me know and I'll make some
12:13	more videos on trigonometry . I'm sure I'm going to
12:17	have some issues where people are gonna get stuck with
12:19	these . Please . If you like the video ,
12:21	remember like and subscribe . Hey and below the video
12:24	in the description there there is the patron feed .
12:28	Their you can always subscribe , but you can also
12:30	actually donate to the tech mouth channel on a video
12:32	by video basis so we can keep plugging these videos
12:35	and making more and more and more and more of
12:37	them . Anyway , thanks for watching . We'll see
12:39	you next time . Bye .

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