 This video is called Soka Toa. I know that sounds like a lot of mumbo jumbo right now and is fairly meaningless to you, but please, bear through this video, write everything down, listen, pay attention, and after this video is done, we'll start doing some practice problems where it really will all start to make sense. So looking here at this screen, you can see some buttons that you may recognize from your calculator. You see something that looks like sin, cos, and tan that you have seen on your calculator. Well, sin is actually pronounced sine and it is a trig function. Cos is short for cosine, which is another trig function and tan is short for tangent, which is a third trig function. This is what they are defined as. They are all ratios where the sine is represented in a right triangle as the, as, I'm sorry, the sine is defined as the opposite over the hypotenuse. So just write that down. We'll practice what that means later, but hopefully you recognize opposite and hypotenuse as being sides of a right triangle. So we will be taking side lengths of a right triangle and you'll have to pick the opposite side and the hypotenuse side. The cosine function is designed as adjacent over hypotenuse. So again, when you're dealing with cosine, you'll be picking two sides of a right triangle, the adjacent side and the hypotenuse side. And lastly, the tangent opposite over adjacent. So we have our three trig functions, sine is opposite over hypotenuse, cosine as adjacent over hypotenuse and tangent as opposite over adjacent. These three things you will have to have memorized, but I'm about to give you a shortcutter at kind of a helpful hint to remember what is what. So like I said, a helpful way to remember this is called Socatowa. Well, what does that stand for? The soak part says that the sine of some angle, I'll just call it angle A for now, equals the opposite over the hypotenuse. So soak, SOH is sine is opposite over hypotenuse. Where the k helps you remember the cosine of some angle, I'll call it angle A right now, is the adjacent side over the hypotenuse. Where finally the tangent, the toa, the tangent of some angle for now I'll call it A is opposite over adjacent. So Socatowa, I actually, instead of writing it like Socatowa like that, I like writing it like this. Some SOH, CAH, TOA. By writing it this way, it helps you remember that you have to make a fraction with the opposites and the hypotenuses or the adjacent and hypotenuse or opposite and adjacent. It helps you remember what goes in the numerator, what goes in the denominator. Really, it's just the order it's written. The first letter tells you sine, cosine or tangent. The second letter tells you what goes in the numerator and the third letter tells you what goes in the denominator. Now some of you might say that's great, but I can't even remember Socatowa. So when I was in high school, my teacher taught me a mnemonic to help me remember and it goes like this. Some old horse, some old horse, caught a horse taking oats away. So you can remember some old horse is your, is your SO, sine is opposite over hypotenuse. Caught a horse is the CAH, cosine is adjacent over hypotenuse and taking oats away represents the TOA, T-O-A, tangent is opposite over adjacent. So like I said earlier, this is something you are gonna have to have memorized. You're going to use it a lot in this chapter when you're dealing with right triangle so it will help you to make sure you know this. So do you have to have it memorized? Yes, but if you can simply remember the Socatowa, if you can memorize that, then you should be able to solve any problem you need. So if you're gonna have to memorize something right here is what I highly recommend that you do. It should be written on the top of every homework assignment for this chapter. You should write it on the top of every quiz and every test because it can help you a lot.