 Let's talk about trigger Properties of triangles Some of the angles in a triangle is 180 for any triangle some of the angles in a triangle is 180 degrees The only triangles you like this pizza. No, I'm pretty sure you like other things other triangles For sure triangles come into play everywhere Do you like music? Trigonometry, do you like light shows trigonometry, right? for right-angle triangles a bc Keep in mind there's six pieces of info in a triangle Pieces slices aren't triangles They're sectors of a circular circular technology But they are related to triangles because triangles are related to circles, right? So triangles definitely are related to pizzas because if pizzas come in circular sizes They're circular shape, then that's trigonometry as well, right because and The unit circle the way we find ourselves in a coordinate is through triangles Right the triangle is also the only shape where the sum of the angles are 180 Every other shape is 360 for this reason triangles have more structural integrity They have and they're that's why you have tripods like tripods are stable more stable, but with triangles Triangles are the building blocks of all polygons Right. It's like the prime factors of polygons or triangles. For example, if you have this Here's a polygon, right? What's the sum of the angles of this polygon? Right That's your hydro Right. Well break it down into into his prime building blocks. It's just the same thing as H2O H2O is H2 and O and H and H right the building block of H2O is HHO The building block of 12 is two times six and two times three Right The building block of this is One triangle Two triangles Three triangles one two three sorry four triangles, right? So there are four triangles that this How many shapes sides one two three four five six six sided polygon is made of right Well, what's the sum of the angles in this triangle is a hundred and eighty times six Right you can break all polygons into into triangles and then from there You can work out their angles or whatever it is if they're regular polygons. This is Not to scale not regular polygon, right? So triangles are your smallest building block of a polygon. That's why they're super important one of the other reasons They're super important, right So take a look Let's kill this as well Triangle has six sides or sir six bits of information Why times six? Did I say times six or did I say times four? Oh, I should set times four poop. I made a mistake That was a brain for it. That was a chicho brain for it. That should have been a hundred and eighty Times four there was four triangles, right? Gotcha. Yeah chicho brain for correct my brain for its police Okay, I make I end up making because I'm mentioning other numbers and other numbers all of a sudden enter the My calculations oops don't do that on exam. Don't do that on homework, right? There's six pieces of info in a triangle, right three sides and three angles and an angle controls the opposite side So this angle This guy controls it. So we're gonna call this capital B So this angle is called capital B and it controls small case B side, right? this angle We're gonna call a because it controls this side and this angle we're gonna call C because it controls that side Let's put the a here too. So we're consistent, right? So this angle controls this side this angle controls that side that angle controls that side Okay The smallest angle controls the smallest side the medium size angle controls the medium side and The largest angle controls the largest side if you got a right angle triangles the 90 degree angle is the largest side Hence C is your longest side Okay, and don't forget gang Free as such free as such free as such Julian Assange is a publisher and journalist that has been crucified for trying to Try to bring transparency and accountability of capital's power to humanity Support him Right. So in a right angle triangle, we have the following other relationship as well Which is the Pythagorean theorem, right? We got one relationship Angles in all triangles equals 180. Hello Mac 650 For right angle triangle, we have the Pythagorean theorem, which is a squared plus B squared equals C squared That's the relationship that exists between a B and C Okay, and C is your hypotenuse. So the two legs of a triangle squared add it together equal the hypotenuse squared That's another property that we have There are three other properties of a triangle Features of a triangle right angle triangle that we also deal with we should call the trig important ratios Right, so three trig Ratios ratios Right, which are sine of an angle is equal to the opposite side divided by the hypotenuse Coase of an angle is equal to the adjacent side divided by the hypotenuse 10 of an angle is equal to the opposite side divided by the adjacent side Okay, those are the properties of a right angle of the trig ratios adjacent side Mac I never like math. Do you suggest a book that makes you like math? Maybe? It really depends what you're into Mac. What's your interest in life? No matter what your interest is in life Mathematics can relate to it All right, if you're interested in business look into mathematics of investing and stuff like this if you're interested in music look into Mathematics of trigonometry really frequencies waves and stuff like this if you're interested in engineering There's tons of books out there and engineering If you're interested in pure mathematics, just look at the algebra as problem-solving Right, we just had a problem. We just did a problem where It was complicated. It was cool, but together we're able to solve a problem So if you like puzzles mathematics is the place to be right So what do the trig ratios mean? ratio is something Compared to something else now remember yeah, there's a difference between a fraction and ratio fraction and ratio The difference between a fraction and a ratio is this I can give you the following Two over three. What does two over three mean two over three means part of a whole Interesting investing yes, I like the math and finance, but it's simple compared to you are explaining on advancement. No Financial mathematics investing can be extremely complicated Some of the most complex mathematics ever done have been in the realm of Investing personal finance right you can start off with some simple stuff But it can go into very complicated stuff mathematics is a tool You can build a shed in your backyard or you can build a skyscraper Right if you want to do a comparison mathematics is limitless And you can apply it into extremely complex levels on any topic Even art like paintings and stuff like this hues of colors and play around with that stuff Fraction two over three is part of a whole so if I have a whole thing I break it into three pieces I'm gonna eat two of them Two out of three right Two parts of a whole. Okay. Thank you. Sorry for no no worries Mac, right as far as math books again Nothing really comes to mind I have certain math books that I've used to learn certain topics If I write down a ratio two over three Ratio two over three is a comparison of two or more things so two over three if it's a ratio it means two circles versus two triangles Okay, it's a comparison right Two versus three Okay Keep that in mind. So these Trig ratios are not fractions. They're ratios. It's a comparison of one thing to another thing Right, and what are these two things comparing? Well the formula tells us what it's comparing It's saying that the sign of an angle, right? the sign of an angle is Equal to the opposite side of that angle Divided by the hypotenuse of that angle of that triangle, right? So I'm gonna erase this part So trigonometry says this if I have a triangle Like this Right right angle triangle and these only work for right angle triangles. Okay. They don't work for non-right angle triangles If this is my theta the sign of theta is the opposite side Opposite divided by the hypotenuse So what does this mean? The ratio why is this important? Well, it's important because of the following if I say that Let's assume. This is 30 degrees right and This is a right angle triangle and let's assume the hypotenuse of this is five Right. I want I want to find this X Okay What I'm gonna do is say Use this formula to find X. This is an absolute It means that for any triangle Right So let's find here. Let me just tell you what sign of 30 is sign of 30 degrees If you punch that to your triangle, you're gonna get this. There's a special triangle called this 30 90 60 1 root 3 2 if you punch in sign of 30 You're gonna get 1 over 2. It's equal to 0.5 Okay Really right here, we're gonna punch it in let me punch it in make sure I didn't do any brain farts here 30 degrees and you're gonna go Sign of that is 0.5 right So sign of 30 degrees is 0.5 Now sign of 30 degrees is not 0.5 Just for this triangle or for this triangle sign of 30 degrees is 0.5 for any Any try no matter how big it is how small it is. I used to hate math growing up until I went to college Ha ha. Yeah, a lot of people right? So if I give you a triangle like this I Say this is 30 degrees and I ask you what the ratio is between this side and this side You will tell me that it's 0.5 The ratio of this side. Let's call this the opposite side and let's call this a hypotenuse The ratio of this divided by this opposite over hype Is equal to 0.5. That's what I wrote down here by the way. Where is it? Right, so if you have one of these you can always find the other one so If the hypotenuse is five you just put five here oops Then the opposite side is going to be 0.5 times five which is 2.5. So we know this is going to be 2.5 So the ratios the trigger ratios are an Absolute for specific angles. It's the relationship of one side of a right angle triangle Relative to the other maybe adjacent versus the hypotenuse Opposite versus the hypotenuse or opposite versus the adjacent it could be this divided by that that divided by that or this divided by that Or it could be this divided by that that divided by that or that divided by that There's six different combinations you could do with this right and That's what the trigger ratios are They're not Some people think these are magic. They're not Right, it's just a way of saying instead of saying what's the really? What's the ratio between the opposite side of an angle and it's hypotenuse? That's the definition of sine theta but that's Too long right as I've said before mathematicians are some of the laziest people you'll find and They try to simplify things and they end up calling these things sine cosine and tangent Where they got those names wrong haven't looked into the history where the name came from I Hope that's clear. Is that clear does that make sense? Would you like expanding on that I Forget who was asked that Trigonometry I'm just going up to see who asked about the Triggs Trig ratios and by the way if you already have The opposite and the hypotenuse so let's assume you have a triangle here Let's erase this Let's assume you have a triangle You already have the two sides or two sides are trying to compare. Let's assume you have this is six and this is 15 and you want to find angle theta well You want to find this angle and The two sides that you have is this and this Remember if this is not 90 degree triangle you can always find this just using a Pythagorean theorem, right? But right now we don't care if we're trying to find theta So if you're trying to find theta What am I looking at mathematics if you're trying to find theta? Well, what sides of this triangle do you have? Relative to this angle you have the opposite side and the hypotenuse so you look at your formulas You go which formula has opposite and hypotenuse? Oh, we got this one opposite and hypotenuse. So just fill in the blanks So you got sine theta is equal to six over hypotenuse is 15 right So how do you isolate? Now the only variable you need to get by itself now is Theta and the way you isolate this on your calculator you got something called second function of the sine sine inverse So the way you separate the sine and the theta you got theta is equal to sine inverse of six over 15 and if you punch that in you'll find out what the angle is and that's the ratio of What the opposite side is relative to the hypotenuse of This angle and if you punch that in here, let's punch it in six divided by 15 and you go Trigonometry second sign is 23.6 degrees So theta is equal to 23.6 degrees. So any triangle that has an Angle any right angle triangle that has an angle of 23.6 degrees its ratio will always be six over 15 which is really two over five point four So the relationship between this side rather than this side that divided by that will be point four All right What does that mean? What's 15 times point four? It's six. So the opposite side will always be 0.4 40 percent of the length of the hypotenuse Okay No, we only open up a black hole and we divide by zero If you divide by zero black hole pops and the universe explodes Right. That's where the black hole comes in from. That's what the black hole is Why can't we travel at the speed of light? Enigma why can't we travel at the speed of light? Do you like sci-fi? I hope you like sci-fi Why can't you travel at the speed of light? for anyone that's like Star Trek Star Wars any any sci-fi infinite mass right If you try to travel at the speed of light you get infinite mass. Do you know why you get infinite mass? I'm gonna erase this