gday welcome to the tech math Channel what we're going to be having a look at in this video is trigonometry so sit back and learn all about it and if you like the video please remember hit the like button beneath the video there and subscribe to the techmath channel so trigonometry deals with this particular shape here a right angle triangle and what it does is it's a branch of mathematics that studies the relationships between the sides of this triangle and the angles that occur within it okay so pretty much we can use say angle here and a side length to work out other side lengths or we could use t two side lengths here to work out unknown angles that's what trigonometry allows us to do so how does it do this well it's fairly simple if we were to consider say an angle here in this triangle so I'm just going to put this down and this angle here is called Theta pretty much what it's saying is this for this particular angle here in a right angle triangle in this particular location in that right angle triangle these two side lengths here would have a particular ratio they would always be an equivalent length compared to one another okay this length and this length would have a certain ratio and this length and this length would have a certain ratio and trigonometry uses this to be able to work out unknown side lengths and unknown angles so how do we do this well the first thing we have to do is we have to be able to label the sides of this particular triangle so in this particular triangle you're going to notice we've got a right angle here we have this angle Theta which we've uh we've already labeled here we also have three sides here we have this longest side here the longest side is called the hypotenuse I'm going to write that in the high pot and use I'm going to put that down as a h here we have the opposite side I'll write that over here the opposite what do I mean by that this particular side is opposite feeter we put that down as an O along this particular side this remaining side which is next to feta we have the adjacent adjacent okay adjacent means next to and we label that with an A so now we've done that as I was saying all these side lengths here the opposite the adjacent the hypotenuse all have particular ratios to one another based on whatever this particular angle here is okay so there's three different functions we are thinking about when we're thinking about these ratios because we have three different ways we could compare the sides we could be comp comparing these two sides to feta or these two sides or you can be comparing these two sides and our three main trigonomic functions are as follows we have the sign function which is the ratio of the opposite and the hypotenuse we have the coine function which is the ratio between the adjacent and the hypotenuse and we have the tangent function which is the ratio between the opposite and the adjacent function function now there's a really really easy way we can remember these uh when we're doing these and this is as follows I'll write this pum monic down right now and here it is some old hags can't always hack their old age okay so sign equals opposite over hypotenuse can't always hack cos equals adjacent over hypotenuse their old age tan equals opposite over adjacent so when I was solving a trigonomic equation pretty much the very first thing I'd do is what we did first off here I'd label these unknown sides the next thing I'd do is I determine which trigonomic function I was going to use so we're pretty much all set now to solve some trigonomic uh problems so let's do that so for our first example here we have a right angle triangle okay it has an angle of 35° it has one side length of 12 M and another unknown side length which we're going to be trying to work out so the very first step to work out this unknown side length is is we are going to do like we do with any trigonomic equation or any trigonomic problem we are going to label the unknown sides so first off we have this long side here which is the hypotenuse then we have this side which is opposite this angle opposite this 35 here this is the opposite so which of our trigonomic functions deals with the opposite and the hypotenuse and you're going to see that it's sign here s is equal to opposite over hypotenuse some old hags so I'm going to write this down s Theta is equal to the opposite over the hypotenuse and now what we do is we just go through and substitu in our values so sin Theta this is sin 35° is equal to the opposite the opposite is what we're trying to work out here x so I'll put that in as X over the hypotenuse which is 12 so we can now work this out a little bit further we could actually say okay uh sin 35 we put that into a calculator we're going to get the answer is 0.57 which is equal to x/ 12 what can we do now so what we have to do is we have to get X by itself okay so X is going to be equal to what now there's a little trick I use here this may or may not help you you may or may not like it okay I'm sure I'm going to get plenty of hate for this but what I do is this when I'm not certain what to do here and I'm trying to solve this particular problem here I just write up an equation next to it a friendly equation as it were the equation I'm going to write is this one 3 = 6 over 2 and we're trying to deal with this particular value here the value up here so what would you do with three and two to get six well you'd multiply them so we're going to multiply these two numbers 12 * 0.57 so 12 * 0.57 and we'll get our answer so if you do that what answer do you get you get our answer of 6.88 M okay so this side length this opposite is 6.88 M and that's how easy trigonometry is to use okay so we're going to go through another example and then I'm going to go through an example where I look at how to work out the angle from uh 29 side length so it's it's a bit of a tweak here so stay tuned for that one as well okay but let's just go through another one of these type examples okay for our second example let's have a look we have a right angle triangle we have an angle of 48° we know that this side length here is 15 and we're trying to work out this unknown side length here so let's label our sides first we have this particular side here which is opposite the angle here so that's the opposite we know that this one here is the hypotenuse that's the easy one to spot so it leaves this one here being the adjacent okay and it makes sense it's the shorter one that's running next to the angle here so which one of these functions uses opposite and adjacent you're going to see here is tan tan Theta equal opposite over adjacent so let's sub in our values now so tan feta becomes tan 48° which is equal to the opposite which is 50 m over our unknown our X okay we can put tan 48 into the calculator if you do this you're going to get this answer of 1 .11 okay the opposite adjacent have that particular ratio of 1.11 for an angle of 48° which is equal to 15 / X so now to solve for x and if you're not certain what to do you might know this straight away but you could do this once again you could go okay 3 = 6 / 2 and we're trying to work out the value on the bottom here the two so that would be 6 / by 3 this number divid by this number this number divided by this number x x here here is going to be equal to this number ID by this number 15 / 1.11 which is equal to how much 1.51 M okay so that's how that particular type of our function in trigonometry works it's pretty simple right now we're going to go through some examples we're going to look at how to work out the angle from s and side lengths it's fairly simple there's just a couple of tweaks with this so in this example here we have a right angle triangle and we know two side lengths we know that this side length here is 105 M and we know that this side length here is 33 M what we're trying to find out is we're trying to find out this unknown angle that would accommodate these side lengths so how do we do that well it's just one little variant and I'll get to that as we uh do this particular problem the very start though is exactly the same we are just going to go through and label whether our sides are opposite hypotenuse or adjacent so we know this long s side here is going to be the hypotenuse we know that this side opposite angle Theta here is the opposite so which one of the functions are we dealing with this is our second thing we can deal with which function and we're going to be dealing with sign here s Theta is going to equal the opposite over the hypotenuse so what is the opposite over the hypotenuse we're going to see here that we have the opposite which is 33 me over 105 M okay so sin Theta is equal to 33 over 105 if we' have work this out what's 33 / 105 you're going to see that sin Theta is equal to 0.314 okay that's just the matter of going 33 / 105 and we get this answer here so what we do now is just a little variant because we have to actually go back we got the ratio we're trying to go back to the angle and you're going to notice on calculators that there's either a second function or something like that that allows you to go from s to this particular thing s-1 okay we want to be using that here we're going to be hitting 3 0.314 and we're going to hit s-1 or second function sign here if we do that we're going to get the answer of theta being equal to 18.3 okay so just make sure you know how to do that on your calculator okay uh anyway we'll go through one more of these examples okay for this example here we have a right angle triangle we have two side LS we know we know that this one here is 17 we know this one here is 12 and we're trying to work out the angle that accommodates these so let's go through and do this uh the very first thing we do is we're going to label our sides we have the hypotenuse which you can see we're not going to be deal dealing with the opposite we're in fact dealing with the adjacent so which one of these functions are we dealing with and you're going to see here the adjacent the hypotenuse is the cosine function so cos Theta is equal to the adjacent over the hypotenuse okay so what is that going to be cos Theta which is what we're trying to find out is equal to the adjacent which is 12 over the hypot years which is 17 so we work out what 12 / 17 is we get the answer of 0.71 okay cos Theta is equal to 0.71 so we're going to be not working out cos we're going to be working out the inverse of cos cos to the ne1 so you're going to hit second function cos and you're going to get uh when you do that you're going to get the answer for Theta Theta or our angle here is equal to 45.1 de so that's how you go doing trigonometry and it's most basic it's pretty simple right it's just those tweaks there and it's also getting to know the calculator that you are using so anyway hopefully that video is some help to you if you got any problems please let me know and I'll make some more videos on trigonometry I'm sure I'm going to have some issues where people are going to get stuck with these please if you like the video remember like And subscribe hey and below the video in the description there there is the uh patreon feed there you can always uh subscribe but you can also actually donate to the techmath channel on a video by video basis so we can keep plugging these videos and making more and more and more and more of them anyway thanks for watching we'll see you next time bye