Maths GCSE (9-1): Revise and learn - Basic Trigonometry | Joshua Bolton | Skillshare

Maths GCSE (9-1): Revise and learn - Basic Trigonometry

Joshua Bolton, Econ Student, Ex GCSE and IB

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9 Lessons (53m)
    • 1. Introduction

    • 2. Types of triangles and their angles

    • 3. Triangle angles question

    • 4. Exterior Angles

    • 5. Interior Angles of Polygons

    • 6. Pythagoras' Theorem Part 1

    • 7. Pythagoras' theorem 2

    • 8. Trigonometry

    • 9. Trigonometry 2

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About This Class

Mathematics GCSE - Revise & Learn: 'Trigonometry'

All Topics Covered with Practice Exam Questions *Up To Date For 2020*

This 9-lesson course includes all the material you need for the ‘Trigonometry’ section of the brand new Maths (9-1) GCSE qualification. Each lecture includes step-by-step examples for every topic, along with worked solutions for practice exam questions.

Throughout the course, I will talk you through the basics of every concept and section, before moving on to practice exam questions. This makes this course suitable for all abilities, whether you are learning GCSE Maths from scratch, or in need of revision leading up to exams.

Course Structure

The course follows the standard Maths GCSE structure (as used by Edexcel, AQA and OCR), meaning it is easy to follow and perfect to use alongside any other learning or revision you may be doing. The course is split up in to the following sections:

· Triangle types

· Angles of Triangles

· Interior Angles

· Exterior Angles

· Pythagoras' Theorem

· Trigonometric Functions

· Inverse Trigonometric Functions

If you follow this course, you will gain a solid understanding of all of the above topics, whilst greatly improving your ability to answer questions on exam day.

Who this course is for:

  • Students revising for their exams

  • Students looking to learn Maths GCSE from scratch (including adults)

  • Anybody looking for guidance and support in reaching their target grade


1. Introduction: welcome to this course on basic trigonometry from the 9 to 1 GCSE mathematics scores. I've recently taken the must GCSE two years ago using the new specification and says, I'm also student. I believe I'm in the best place to help you. I've been tutoring for two years now, and I hope that this course will help you manipulate fundamental concepts of basic trigonometry. This course will help you to reach your maximum potential and achieve the best GCSE grade you can. On completion of the course, you'll have more confidence in answering basic trigonometry questions. The common in the new specification. We'll go through a number of modules, including triangle types, interior and exterior angles. Trigana Metric Functions on Pythagoras Theorem. I hope you enjoy this course as enjoyment breeze. Engagement on engagement is what will help you to achieve your best grades, I hope. See soon 2. Types of triangles and their angles: in this video, we're just going to look at the different types of triangles which underlie. The prince will have a lot of mathematics because a lot of problems that you encounter in GCSE involve knowing the different triangles. So firstly is important to remember that the sum of angles in any triangle come sums. This is what means they all are together 280 degrees. So all of the angles in a triangle without to 180 degrees, let's have a look at the different. I was trying to see an equal actual trying. No, that calm Jesus CBO definitely see them occasionally as the equilateral triangle is workers equal as the name stays, all of the sides are exactly the same length. And since all of the sides of the same name, it means that all of the different angles these three angles are the same because the side , all the same things, say, since she never the Azeri mention before the summer any of angles in any triangle, some 180 degrees near the 180 degrees divided by three cause there's three angles, so all of the angles and triangle add up to 100 degrees on this three of them. So we know each angle was 60 degrees, 60 60 very low degrees, right? The next top trying we have is a nice softly strangle. These are more common because obviously, the GCSE has got harder. More recently. So here's the so cities triangle in this, the Socialist Triangle has two sides. They're the same. So in evidence, these two angles are also the same, so this would be a different angle. So let's just say it's his eggs. So X is just any value. So therefore these just to make you clear the same angle. So just do a demonstration in here. Say, for example, this and I socially, strongly might get in examining mighty six centimeters, six centimeters. So these are the same length on then. You know, this is nice awfully strong because these are the same thing. This might be eight centimeters from that. You know, these angles of the same. C'mon, get told this is 30 degrees and then from that you know that this is also 30 degrees because these angles after the same cause, he's linked to the same. And then from not if you need to work out, say what this was. You know, that is 180 degrees once, two times 30 because 108 degrees is the some cool angles in a triangle. Andi, you take off the other two angles, which is the to 30 degrees, which gives you 100 20 degrees. So this would be on 20 fear Going to work it out on. Lastly is the, um most common type of triangle you're gonna see is a scaling triangle which is just all unequal sides. They usually will happen. It will be given each of these angles. So when you see a scaling triangle, you'll just have to use the knowledge that all of the angles well, some 2180 degrees. Just remember, that's a really important fact in maths. On designing remember, I help you for the majority of these questions where especially scaling triangles will get given multiple angles. But just remember this fact and this is definitely keep want to take away from this video 3. Triangle angles question: Hey guys. So obviously we looked last time in the equilateral triangle. They are so slowly strangle on the scaling triangle and how, in any triangle, it's a trunk angle some 2180 degrees. So if you guys will remember these fags they wanted Teoh just show you the next where this could actually be useful. So one question I've pulled from the EDEK soul textbook is this. So and as you've to work out, why is these lines as I dreamed for me in that these two sides the same length? Hopefully, by now you've already identified. If it all, that's fine. But this is a nice sausages triangle, because these two lengths of the same, that means that this angle on this angle to it let's call it X and eggs are the same were given that the top angle was 42 degrees. So we got more gown. That's two X, say or less right as X plus X, because there's two lots of these exes. So that angle, plus that angle plus 42 degrees is equal to 180 degrees. Now we can say that two X because it's just There's two time to lots of these. This angle, because they're the same, equals 180 degrees minus 42 degrees. Because you just want to work out what the individual bottom angles are here. So then we can say that two x is 101 138 degrees because 180 minus 42 years. 138 Andi Then, since there's two lots of actually can work out what X is by dividing 138 by two. Because that will give us what exactly one live exists because that will show us how that will show us exactly what one angle is. Because right now we've got both angles. This is to Angus. Was Regis anyone? So this there for all we know, that X is equal to s o. Let's thing we seven see, Yeah, say be 69 degrees now Really other. Another really important factor of maths. That which will use a lot and mocked was arias. But you start using it subconsciously. Is that angles on a straight line equal 1 80 degrees to say this is why and this is eggs. These two angles equal 180 degree. So why I plus X equals 180 years, all angles on a straight line, equal 100 degrees. That's a given is really important in maths. So from this surge in L. A X equals 69. Now the 69 plus y equals 180 degrees. So that's using the idea. So is gets right angles on a straight line, equal 1 80 degrees. Therefore, we can finally say that why is equal to 118. Minus 69 equals 111 degrees. 4. Exterior Angles: Okay, so today goes in religion exterior angles. The last time, if you're only we looked it Interior angles to exterior angles are effectively the angles. There, just on the outside of the shape, hands the names of the opposite of interior se. It's a bit weird of a weird concept, I think, especially as a student like. But anyways, if this is an interior and gorgeous drawing reds, the US conceive E the exterior angle Is this okay? So you basically have to extend out on draw. The angle said. Look like these. These would be a little of the exterior angles now, if you notice the interior angle plus the exteriors. Interior plus exterior adds to wanting to degrees because it's using what we learned earlier than the idea that angles on a straight line sometime on 80 degrees just seem by this more first, you can kinda see that this is, ah, the interior and the exterior angle labeled, and they sometime 1 80 degrees. Let me just said, Say, that's pretty clear on some of exterior angles. In a polygon is always 360 degrees, I say, just bringing out the safety and moves you this, huh? So all of these all of the angles. So these red and was just a common she one of these uncles, some to 360 degrees, always exterior and was always something doesn't matter. The shape there was some 360 degrees se toe workout, an individual exterior and go. You have to then divided by the number of sides. So this is a Pentagon. This five sites. So you would do is you just a 360 degrees divided by five and that will give you the that would give you each Xterra. And so, in this case, because it's been going to be 72 degrees says effectively how you work out, Um, the exterior angles in any shape so we can do one more examples Or is she? So if we take into account a hex again this time you to take a second? Just think about exactly how the Xterra angles might look like. So probably by now you're thinking, why would they might look like well, anyway, hit for your right or drawing another color just to show you. So you just extend a load of these own Sorry, for the on a zero extra, and also the interior is ahead. So I drove. There's a black loaded with the exteriors of here, and all of the interiors are here. If you were a is already there or the if it wanted that I would give you. If you're worried about messing up like thinking, you might draw on this side. If you end up during a semi circle or it's 180 degrees is the wrong side, just right on the other side of the extension of the line. You always remember it that way. So you see is obviously a hexagon. Six sides. They're full. So this these $3 I use in maths, it just means that four year, that's all. It means that the exterior it's a Southern next area is, as we said, 306 degrees, always for any shape, 360 degrees hands you just do 360 degrees divided by six. He was 60 degrees rights. Each exterior angle in a hex gun equals six degrees. Thanks for listening. Eyes will see next time 5. Interior Angles of Polygons: So today we're gonna be looking at the interior angles of polygons. So a polygon is just basically any shape, really so has taken to counting Pentagon. First, let's ever think about what interior angles are so interior angles, all of these angles inside the shapes interment inside. So there's a formula that you're going to need to learn. It's always best just to learn these cause in GCC. Now you do not get formula. Booklet on also is about the speed of which you conduce thes things in your head so quickly that you couldn't know these formulas. The quick you need the questions in the exam especially. There's a lot of time pressure se formally need. Today is the sun of angles with a shape within shape with n say ends just any number, any number. Basically, number of sides equals, and there's n minus two times I 180 degrees. This is really important formula guys and should just try your best to learn this formula and they'll come the more you use it. So So if we take into account our Pentagon again No, one day there we go. If we take new on the Pentagon again, There's five sides. See, because ends the number of sides, say, or you did you put into Foreigner five minus T times 180 degrees? Because it's five sides in the shape San equals five just made that clear. It says three tons 1 80 which is, say, 300 plus to fort equals 5 40 Just make it clear. I just split up the 100. So did three times 100 then 80 times throughs on out of these together. So you basically it worked for any. So even if you hadn't aren't gone or so not guns? A. So we'll just do a quick question to make it. Make sure you guys understand this se. It's an exam style question taken from the addict sell book. The diagram shows regular hexagon on, and so just make sure regular doctor calculate the size of the angle Mark X. You must show all if you're working, so we look to the interior angles. So another point the is really important. GCSE maths Is that the angles around a point, saying Bronson, who 3 60 degrees. That was like a circle. If you look at a lengthy angle in a circle, he adds up to 36 Yes, that's the entire circle. So 1/4 of it is 90 degrees. Soho suckle was 3 60 degrees. Just really keep going. But you guys probably ordinate up from early years. It is no one to this question. Se. We need to calculate size X. So X is just on the outside here. So we you sends, you know that angles in a circle at 360 degrees. Here's a circle they had to 3 60 degrees. You need to work at this angle on this angle, and then you can use, though, in order to find eggs. Because all of these three anguished let's call them Y and zed. Just get rid of these lines, ones that at 3 60 experts Wiper said, That's 36 degrees now what have we learned earlier on? Say, you know, I was in the tri angles of a polygon. Add up. You can work it out, using the formula M minus two terms 1 80 and then dividing it by the number of angles, right? We'll give you an individual angle. Say it's taken demands. He got a hexagon on gun Octagon. So Hexagon has six sides. So if we dio six substituting six into this year, full tons 1 80 equals s a Let's just think about it for 720 degrees. And now you're gonna divide it with six because they're six angles in the hex gun. So this will give us why? Because this is the hex given slated age. But this one, I so basically so each angle so well, I would then be equality 7 20 divided by six 120 degrees. Results could you lay without 120 degrees? Now we've got said says that is an octagon. So we just substitute is if Octagon opt eight minus two turns I 1 80 degrees six tons 1 80 degrees equals are just using so 1080 degrees. And then, since there's 88 angles because it's an octagon, same number of sides angle. So you just divided by eight will give us said which is the individual angle. So you divided by a is 135 degrees That fool that, um, we can say the axe so 3 60 degrees equals x +135 plus 1 20 So just using simple out over which you guys would have done earlier in the book and say the X is equal to 360 degrees, minus 135 minus 1 20 and that is equal to so if we just consider the 15 than the 1 20 against 15 which is the fine lines up from this I hate that has helped you guys, but this is a choir typical style exam question, but they might use differ different shapes. It's really important you just remember this formula. The M minus two times, 180 degrees and that will give you that will give you the some of the interior angles for lazy, different shapes. Some of interior I'm moves for putting. You guys can learn to that and see next time 6. Pythagoras' Theorem Part 1: I guess it today, guys. The blood song, such as it does look a trigonometry. So it's trying to get a little bit harder like, but trigonometry is actually not as bad as everyone makes out. So, Saul, if you guys have probably heard of Pythagoras theorem so this only works for right angle trying or so right. Angled triangles. You problem Name trying on 90 degrees. This is 90 degree angle. This is wrong. We're trying no relay with the sub day on this side B. J sorry. And they see python gris is theorem Is that seesk? Words is equal to a squared plus B school that so this value squared equals this squared Plus this squad. So when we have to doing just get rid of that on this one says today is basically use this in a variety of ways and recognize when you need to use existing to anyone, right? Angled triangles You contested for triangles, right? Angled as well. Yeah, you just substitute the values in. So we'll do a few practice questions so that basically Anderson sound the prince will wait . It's relatively straightforward. Usually would use a calculator because to your papers are calculated paper to make three so most of time you'll have a calculated to use. If not, the numbers were pretty simple. So currently, the length of the hot pot, a new SoHo Potter news is the longest side is usually this one says, opposite the right angle. So here's the high parts initials live. Hate in each trying on give you a chance to three significant fears. Seeing using the currency see, in this case is hate. So you can say they hate Squared is equal to six. Good cause us A plus seven squad. So if you guys know your times tables, Hate Squared is just equal to 36 plus 49 to hate Squad is purely equity 17 85 the census sister squirt to find out. Just hate because it's just asking us to find the length of high potty news because it's currently hate squad. You need to square root because that's the opposite of squared. So he just just equal to re 85. But it says give you answers. Court to two significant figures so necessary. Use a calculator because it's got the calculator. Cymbalta. We just used 3 85 you get 9.2195 and, like summary long numbers, say, nine point 2195 Dirty did it. It's really important. You know what two significant figures are. So basically two significant figures are the two main parts. Se Mattingly. In this case, it just be nine point to the euro entity. That's two significant figures he usually right in like this. Just to clarify, say, if we had one a 3.781 it's two significant figures. This would be 100. Just carve away because you and you have to look at the base significant parts. This would be three significant figures. You have to make that zero so weird concept, significant figures. But you get usually pretty quickly. And if you guys need anymore explaining, just drop me a line a new to me. So that's verse on page is equally important to, for the 2nd 1 is much saying concepts of the high. Puccini's again is opposite the right angle. This is the hard part E news. So you do the same thing in hate. Squared is equal to nine squared plus four squared. You know, your times, tables Ah, hey. Squared is equal to 81 plus 16 equals. Um, surgery 97. Say, hey, ages equal over 97. Bring this into the count late. You're going to get sometimes I'd known calculating you guys using. But there's an S two D button which will allow you to convert from fractions. Did well search to destiny. Say is we get 9.848 So two significant figures. Hopefully, you guys can. This one. What do you think it be if you just give it a second to try and think about it? Case it probably be 9.8 centimeters. Never forget your units. I think I forgot to buy, kid. But make sure you put centimeters because otherwise they can penalize you for not having the units to make sure because they've given in centimeters to make sure you remember that . See, look, they try and treat you because it says meters. Be very careful on the units they here. They give you decimals for the idea. Just the seems that I bought in uses opposite. But this is then any this is being so uh only does the same things that c squared equals a squared plus B Squared se is of shooting into hate squared Leslie with hate, which is the high Potter news us We're labeling, hates to make it nice needs to remember And the Examiner can see that 6.2 squared plus 5.1 squared. Now I can't do so My head Like I'm sure some of you guys want me to. I can't. It's a fun one school and we get 64 145 se Teoh Two significant figures. Say sorry. First go to square you 64.45 to square on the couch later. 8.28 eight point Teoh. Two significant figures a point, i meters because it's different units Mama like up there. Two significant figures they get in that you're fine lines of phone so lost, so you can just do a quick exam. Question one. Just minimize that dance is easy toe around. So here we have Ah, Schepisi. Um a b six centimeter a ks And I say we were labeled it for us. Calculate the perimeter of a B C D. So the prince is just the edges. You guys probably so proven toe edge, you guys prompting RG three months. Pretty easy question because your stores look at the marks and I'll give you an indication . Three marks equals roughly three minutes, but one month for a minute. The quick he worked better. So primitive. Give you honest Correcto. One decimal place. There's another key part. You got dogs marks off it. So for the printer, it's just all of these. So you don't need to walk up. Basically what d. C is yours? My thing. However, nothing we can do that book. This is where I love mascot. You have to kind of think about how you can solve a problem because we're in trouble. So if you draw this line down here, you get a right angle triangle on. We worked out using my progress with the hippopotamuses because we know that this length of B six cause it's the same on this length, would just be safe. This is a in this hobbling this 12. The difference between this whole lengthen This holdings at this distance is four centimeters. Because if you can see here of just on the I've just on the 12 minus eight is this is 12 and then the small side dates. A. You have four centimeters to the difference. Therefore, the proof is effectively 12 said this side plus six, which is this side plus a should that side and then plus D. C. Which is we're about to work out because that's the hype artiness say to work out D. C. If he uses the try and go save in a four squared plus six word equals hates good to send thinkers. Look, this is the right angle opposite the Ryan with his our parties so foursquare the 16 plus 36 equals hates good. Someone just going to get 52 equals. Hate squad say Cheek was square of 50 t. So now we need to do is the perimeter is equal to 12 plus six plus a plus Route 52 and it said, give it to one decimal place. We got to remember that I say, let's could you have some topless six for a 1st 3 52 33.2111 equals 33 20 toe centimeters to one decimal place. Certainly you guys get that and ah, see, next time 7. Pythagoras' theorem 2: there's an extension onto the Pythagoras section that we looked at last. I'm sorry. It's a bit long, guys. So put Congress there. Um, let's call manipulation. So, basically, sometimes this formula for I see a day the C squared equals a school crispy squid. Sometimes what they will want you to do is to really be able to manipulate them. So is only right angle triangles re said. And this is the high Potter news, and you always have to remember the way in which this is labeled se. Um, basically, I will now show you an example where they want you to manipulate it. So in this case, here's the wrong When this is the high party news. So the formula now you can start right out of the same still hate squared equals zero is just sea squirt. Put it see, to make it easy, seeing hey be it's kind of just a convention. Actually, the, um the angle you have is the big letter on the opposite you have is a small letter like would you see later on to be the big B, which is where this is small being an opposite the sea angle you have a small C So basically conventions still the same there for the side says C squared equals a squared plus B squared. But this time we don't know Be so you see Mr Wright's out See 15 sward is equal to a sward is tense words who nears 100 plus b squared? No, we have to rearrange it. So using some algebra, you can see the 15 squared minus 100 Because you've now minus this You moved over to the other side seam mine. Nestor, To get rid of it on this sudden and goes into the outside equals B squared. So be a is equal to the square root of 15 squared minus 100 because you have to square rooted to get just be so put onto a calculator or we're gonna get is 15 squared The score 50 good ones 100 is 11.18 and I think is it two dozen places to room, which has that would be fine. Well, you get 11 when 1803 very surrounding it it just goes to to this one place is quite easily case of uh thanks for listening. Special video goes Nazi Next time 8. Trigonometry: Okay, so you know what you're getting into? Trigger Norman tree right, Which goes a bit more complicated. So well, the death of trigonometry silly and Ryan who? Trying room. So if the truly you've got your right angle, Angie also need to be able Teoh label the other side. So let's make a little were before about this is the high part in ease because it the one office ill they're writing was always our fortunes. However, the other hang the other side's change to these, the two other side, this side and this side into change with their names. So it's relevant. It depends on where the actual angle you're looking is said. Theatre is just any angle. So use that, say, an angle Justin angle. So the side opposite the angles just called the opposite underside between the the angle on the right angles. Cody and Jason just always really important to be able to recognize thes besides, because you'll need them a lot in trigonometry. So say, if I gave you another triangle like this, you hear? This is the angle. This really opposite. This will be the high part in ease, and this be the adjacent heavily. You guys can see that I have been clear case and I got some questions about these. Uh, sorry. First we need Teoh just before we go into the questions. Took a few different things. So the reason that I told you Teoh know about adjacent High Potter news and the officer is cause you need to know a sign co sign, Do you say cause and turned? She's the three things you then use that triggered a metric antes that you were used to work out to do trigonometry, basically the fundamentals of trigonometry. So there's a sure reckoning that you're gonna need today to the sign oven angle so the angle would be Theater is equal to the opposite over the high parties, the cause of the nine boom. So there's always between zero minus one this cause and sign me for GCSE level months. You just need to remember these on the more you get, the more fluid it will come. Is it good? Teoh Jason over her puts news unless you have turn which is equal to officer over Jason. So basically can utilize these in order to calculate what you need from question. so yeah, you got this is the angle for Chinese is the angle that's the opposite. And then a Jason, send your use these on the angle toe, work out the different things is if you native, they will use different. Um then use two of the three. See, you have to identify which one to use the way you should. Remember. This is so, huh, toe. So I was remembered it and really help say you're on soccer toast. They saw sign because upset about what you saw. There are reports news cause equals a Jason Neighborhood parties and tonic was opposite over adjacent. It's a really good way to remember. It's just keeping that to yourself. So let's have a look. A question. Shall we? Teoh. We have to calculate this value of X. So whenever you see a question like this, the first thing I would recommend for you guys to do in exam is just because it really doesn't take long. Is three months take less than a minute? Let's just lay both sides. Here's your I am ghost. This is theater, and the examples I've given its opposite is this easy. You would know that the side opposite the right angle is the high parties on that make this the adjacent. So now the important thing here is realizing that you've got given the length here and you gotta work out this one on. This is the angle you've been given, and no point you given what is so it doesn't effectively matter. So this is what you need to be careful whether you identify whether you sign cause or town to using soccer tour. So the over Hey, age A of age. So car tow A. So basically, here we're using the high Potter news on the opposite. So what was the high parties in the opposite? That sign, then using son, you just say this sign of the anguish of 60 degrees because we know that now because we're giving it is equal to opposite. So in this case, as X So you were doing is a substituting in over hate, which 32 centimeters. So if we need to work out, what X is well, we're gonna do is using some simple Algebra. X is equal to 32 times by signed 60. It doesn't really matter if you don't use the brackets by was like Texas Good convention se because all we're doing is you're multiplying through by 30 t send. All we gotta do is put into a calculates. They want to get three significant figures, say, 30 t you see? Sign you see the sign button on your calculator on Do you just put it in? Put Remember your brackets and all you get is 27.71 to 8. 27.71 Teoh Syria was three significant figures, so therefore X is equal to 27.73 Run to this, the third significant figures, see? And it's once around 27 was a centimeters. Always remember your units. Okay, say, here's another question calculates question. But any exam, Sometimes you'll get scenario and in these scenarios is yes, mentally a real life scenario on you've got to really think about about what it's asking you to do. So Ladder is seven meters long and is leaning against the water here. Let's just or I walk. I really recommend you just draw a sketch. Makes life so much easier. So here is your ladder little executive, really? But there's a Lada and its seven meters long and the angle of elevation is 72 degrees. Got so those elevators 72 degrees easy. Well, natives is here. We have a right angle drawing on weaken. Just use our knowledge. Says trying to find out this high se At first the question is complicated. Doesn't give you anything, but all is really asking you to Dio is calculated using trigonometry, which is just signed causing town. Say, this is the high Potter news. This is the adjacent cause and then you got the opposite is the opposite is the height. So here all this asking us to look for, say sign cousin town Do same soccer tours over hate every age on over. Therefore here we're trying to work out the height. Onda we So is the Hope Water News. The officer earned the angle. See, as you can see because it is the hope, what's news and the opposite, which she's unsigned. It's a sign of 72 equals, say, opposite overhype 40 news, which is I would just say hi divided by seven. So sign 72 multiplied by seven cause which is multiplying that three equals the heights is its status three significant figures. No, Just as the icy yes, basic convention that you always use the three significant figures. It's usually tweedy. And we get 6.6573 It's a height equals 6.65736 equal. 6.66 cause obviously around because this is seven. And is it in meters? It was you and always goes at the end of each chance that you get just kind of look back And you think 616 minutes. Okay, that makes sense in the scenario, this is seven meters, just kind of common sense. Check it. Because if you're getting 1000 meters on a seven meter lied us something from wrong, say, then you go back and just make sure and check a gay. Thanks again. I've seen a some 9. Trigonometry 2: Hey, it's the last week. We're looking at a loss actual ing and trigonometry. So we're gonna go back a look a trigonometry. And in the last section we looked mainly at cases which looked like this. What we had an angle given to us aside, hits calculate and unknown where this could be the height of the war. But basically, with Coughlin onside and in this section, we're gonna take dripping onto slightly further. So it's gonna get Simon complicated, but go through it slowly and hopefully with a few examples as well. You'll start to understand the concepts better. It's the kind of ideas we're gonna look at today where you've given to side So that Z six centimeters on tour centimeters on your given an unknown angle. I'm really is not that different, Teoh, what we're doing last week So you still have to identify using soccer toe so would shred uh , right now here they saw Okay, uh, toe, you have to identify with the you need sign cause the town which was fatally we did last week. Given what you know, se once you can identify. So firstly, label was we didn't force this The opposite. This is the adjacent because this the rangel on this the hope Rossini's don't you know, this is what you do is you would look at the you look at the two that you know. So here we know the officer on the adjacent, So obviously the one that uses the opposite Jason town Here we identify that we're gonna use time, and here's where it's different. So when your trying to calculate an angle, you know, the time of the angle what you'd usually put in is equal to opposite over adjacent, right. So in the past, you'd substitute all the values in you'd get ton 45 equals, then this We use the previous example to make clear. You get 10. 45 is equal to, and it be opposite over adjacent to exit for seven. And then you're sold facts. And that was easy of in this snow. It's gonna be slightly different. So we know we don't know the angles we're gonna write. Town theater is equal to hi. And then you're just gonna put in So the opposite here six and the adjacent is 12. So you could always him for down too 1/2 religious in any manner. But anyway, in this case, when you don't know the angle, you can use an inverse function on your calculator. It will look like either sign once one rockets cause minus one. Brock is or town once. When work is and you see this online calculator and what you're going to do here as you do the inverse of the time minus one, you input. What? This is the opposite over adjacent to your emperor opposite over adjacent. He'll give you the angle theater in degrees. So let's do for this turn of minus one, right? So if we put in ah, half and if you just go to your calculator in turn a minus one was there a point for the same half is 26 0.565 states. Three significant figures is 26 16 degrees, so that would then give you the angle so it just you basically have to use the same methods re lump for and using sock. It'll identify what you need to use and then use the inverse function, replacing the angle with, um, the opposite over adjacent or office over Hope Watson use etcetera, So this morning we clears, we'll do it. An example first from practice Question se here we have a question on as usual, we first have to label the triangle as you Wednesday. So here we know that this is the opposite causes opposite the angle. How fortune use opposite the right angle on the need. Jason is between the right angle and the angle. Say you have to calculate size the walmart degs. So first you have to identify what you're going to use. So in this case, we have the adjacent on the high part in use that we know. So using soccer teller, which guards were probably being familiar with. Now you know that we need to use cause cause I includes the adjacent I potties. Here we do is cause minus one because we don't know the angle of a Jason. A vibrant sneeze at the adjacent 6.4 over 9.6. Justin put this into a calculator and you should get a number that basically will be the angle X. So we're not one. Sex the into your calculator and you have 48 points one a mine. It was 48 point so I asked. My 48.2 degrees, 23 significant figures is overly as little work, lira. A lot of the time in the maths GCSE. They also ask you to know the values. This is something that's only really common to the new maths GCSE, and it's quite difficult to do, I think. But the more used them honestly, you will get a question where you will need to know them. So say if you know, if you get given Anguilla's 30 degrees and you're asked to work out six and you need to work this out since, you know sign of 30. So which would you say? It's 1/2 cause sign of 30 as you know, is equal to the opposite overhype water news from soccer toe send you'd substitutes and 30 cause you know it's Equador half into opposite which in this case would be X. I have ah, the yes sir six and then asked to solve for X. So in this case should just to cross multiplication, you get two X Z equals six X equals three, so you could be asked to do it without a calculator, and it could go on and non calculator people just don't bounce up. Mind, though it's extremely easy to remember especially signing cause Which of the kind of name ones, If you just put in the time to memorize it, say a trick that I always use. It's safer. It's for sign. Always remember, it's does say, for zero degrees. It starts at zero. 30 45 a 90 60 story than 90 degrees. So the way that I remember this is always increasing for sign and you go to think about the numerator is to me they're all over, too. He just got from zero C zero. Then you go one ever t so increases to one, then route to over t So was the re, but really one of one is one, so you just don't include it and then read three of three. So you're doing is you're just throw over. Three of to see is always over two and you count up square ease and then eventually gets a warm No, if you know, sign you automatic in their cause because cause is just the reverse of sign. Say you start one and then it goes to read three over tea. So this is for 30 degrees cause of 30 degrees. So you're just using this table of effectively one world drum effectively drawn out for you . Then you can worth out. All of the different angle say cause of 45 is richer. Vitter's the same for both because it's just going in reverse. And then this is 1/2. This is here. It's just the opposite town is one that you effectively will just have to remember. Unfortunately, as town is effectively one that you just have to remember because Thanh is very different. Say 10 90 0 in town of 45 is one these two that the ones that get confused Teoh ton of zero , If I remember rightly. Yeah, Talent. Sorry. Time online. She doesn't exist just in finance. Anton A 00 So these are the two that I get confused about. Say, you have to just remember that this is room three on the other One is Route 3 83 Voice is no easy way to remember this guys, and you just sort of put in the time to memorize it on does for quite sign and cause they're the best tips that I've gone. I hope this helps she Thanks