 Hey, welcome to the second video in our series on trigonometry for electricians in this video We're start getting into trig functions sine cosine and tangent But before we do that what we have to do is name the sides of the triangle We have this side here, which we discussed in the last one is always going to be called the hypotenuse But this fellow and this fellow they have different names now It's all going to be based off what we call our designated angle now You see this little funky Greek symbol here We call that theta and in this case. This is my designated angle So let's walk through how I name these sides based off the fact that this here is my designated angle We know that this is the hypotenuse There we go Now we have our designated angle sitting here and we have our side over here, which is sitting opposite of that Guess what that side is called? Yep, that's right. That's our opposite side Now we also have this side that's sitting down here that is sitting adjacent to the theta symbol or the designated angle and yours I said adjacent so guess what that name is going to be? Yep, you guessed it adjacent Now that's all based on the fact that this theta or this designated angle is sitting here Now, what if we moved it up to this side here would that change things? 100% yes now the hypotenuse is always going to be the hypotenuse because it's the longest side So that didn't change but this side and this side are going to change names Let's move that theta up to here. Our designated angle is now up top up top Which means that this stays the hypotenuse Now here comes the changes now this side, which used to be the adjacent is now the side that is Opposite our theta or our designated angle and this side over here Which wants that opposite our designated angle is now sitting adjacent to our designated angle now when we start dealing with these things We're going to talk about the ratios of the sides of the triangle and how they're related to our designated angle They have all have ratios each side here has a ratio Which will help us determine what this angle is So let's flip this triangle back onto its side here and make this our designated angle and talk about these ratios Now on this side, I've got my designated angle. This will be my opposite This is my hypotenuse and this is my adjacent if I want to figure out what this angle is somebody who's smarter than all of Us has determined that the sign of this angle is equal to the ratio of my opposite side over my hypotenuse Now that's not where it ends. There's others We also could say that the coasts of this angle or the cosine of this angle is equal to our adjacent over our Hi pot our hypotenuse say that five times real fast the ratio of this side over this side That is our cosine. We've got one more We can say that the tangent of our designated angle or the tangent of theta is equal to our opposite Over our hypotenuse and those are the three trig functions. We're going to use we're going to use sine cosine and tangent and there's an easy way to remember the Ratios instead of having to have this hard memorization problem. We can just come up with this mnemonic and it is this I'm sure a lot of you guys know it So katoa So sine is opposite over hypotenuse. Ka cosine is adjacent over our hypotenuse and toa Tangent is opposite over adjacent now. You should never forget that. I'm sure you actually already knew that coming into this Now as we did in the previous video, let's start throwing some numbers at this and playing with this and figure out How we can determine angles? So let's use the common three four five triangle here You can use Pythagoras theorem to determine that three squared plus four squared equals five squared It all plays out from the last video. You can do you can prove that now What we're trying to do is determine what this angle is because that becomes very important to us in electrical theory later on Now we can use any of those three trig functions sine cosine or tangent So what we're going to do is walk through with all three Let's start out with sine the sine of this angle is equal to our opposite over our hypotenuse So sine theta is equal to four over five So let's just write that off on the side there The sine of theta is equal to four over five Now let's get rid of that four over five and turn that into a number we can deal with the sine of theta is equal to four divided by five Which is point eight? So now comes the tricky part. We've got sine of theta is equal to point eight But we don't want that sign there. We want to get rid of that We want just to figure out what the theta is or what the angle is So what we're gonna have to do is use your calculators and if you take a look at your calculator You should have trigonometry functions on your calculator if you don't then you've got the wrong calculator on you and If you have a smart phone, you can probably just take your calculator out and if you lay it on its side It should pull up some trig functions But let me show you a picture of the calculator that I use when I'm teaching this stuff So what we need to do is find your inverse sine now if you look at this calculator here I've got my trig functions up here sine cosine and tangent. I've got Sine right there. Now if you notice up above there, I've got sine to the negative one. That's your inverse sine Now I've got this second function. You see it's been worn out. So use it quite a lot. That's like your shift key So you press second function inverse sine point eight or depending on what your calculator is It might be point eight second function inverse sine every calculator is different So you'll have to get used to it on your own But that should get you the answer that you're looking for that will get rid of the sine So inverse sine point eight will give you the angle which is 53.1 degrees. So there you go. We solved the angle. We have solved theta using sine, which is our Opposite over our hypotenuse. Now we're gonna use the other functions as well We're gonna use cosine and we're gonna use tangent and hopefully This angle should work out the same using different ratios. So let's take a look Using cosine of theta same idea All we have to do is take three divided by five because cos is adjacent over hypotenuse So we take three divided by five and that equals Point six. So the cos of theta is equal to point six and again using our calculator We want to get rid of the cos so we're going to inverse cos that let's take a look at that one So just as we had before we're just going to take the second function and we're going to use cos So it'll be a second function which gets you that inverse cos So again, we'll point in point six second function inverse cos to get our answer or perhaps depending on your calculator It's inverse cos point six Anyway, you look at it. We're going to get an angle of 53.1 degrees. So we have determined using sine that we can get 53.1 degrees We've now used cosine that leaves us with tangent. Let's take a peek at that one Using tangent we use the formula toa Tangent of theta is equal to four over three opposite over adjacent So the tangent of theta. Let's turn that into a number is going to equal 1.33 and again, we want to get rid of the tan so we have to inverse tan that out of there So let's take a look at our calculator one last time. So let's take our button here and press inverse tan 1.33 Equals, which is that guy or you're going to put 1.33 Inverse tan again depending totally on your calculator and you should get your angle Which we're hoping is going to be 53.1 degrees. Aren't we? Let's take a look Well, what do you know it is 53.1 degrees? So there you go We have determined using any of these three sides using either sine which is opposite over a hypotenuse cosine Which is adjacent over hypotenuse or tangent which is opposite over adjacent using those fun trig functions We can use it to determine the angle and that's what we're doing with this one Now what we're going to do in next video is determine how to what to do when you've got just an angle and a side How do we work that out? Hopefully this was helpful if you have any questions at all Please leave a comment in the comment section and we'll see you in the next one