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# ACT Trigonometry

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So hopefully I'm not outdating myself too much. If I tell you that when I was in High School the Makarena was really really big. You probably have heard it, you know with that dance that goes like, right, okay. But here's a question who's the artist who wrote the song? Everyone knows it, everyone knows the dance, who's the artist? You probably have no idea, let me tell you why, they never made another song that was a hit. So that's called a one hit wonder and in this episode we're going to talk about one hit wonders on the Math section. They're always going to be some questions that without fail will show up one time. And they look a little complicated unless you know exactly how to do them. So it's kind of like... if it's easy to learn why not learn and you can just nail those questions which you know will appear. In this episode, we're going to take a look at four one hit wonders and then afterwards we'll take a look at SOHCAHTOA which is a trigonometry question that can help you easily answer two out of the four trigonometry questions on the ACT.

Four one hit one hit wonders. You're always going to see a question about the fundamental counting principal, a question about matrices, a question about the equation of a circle and a question testing if you can find the area of a parallelogram. And you may be thinking oh my God I don't know how to do any of these things it just sounds really complicated. The reason I picked them out is 'cause they're actually very simple to learn. So we're going to quickly go through these and you'll see how you can really easily pick up these points on testing.

First, fundamental counting principle. Here I am in my closet deciding what to wear. I have 3 skirts, 5 shirts, 6 pairs of shoes and 2 pairs of socks. If I mix and match these elements, how many total different outfits can I make? An interesting question you've probably seen under the practice test. So okay students do all sorts of things you know, making a list of how many actions they have, no need. The fundamental counting principal says you just multiply all your different options and that's the total amount of combinations that you have. So here we go, it's just 3 times 5 times 6 times 2. Okay well 5 times 6 that's 30 times 2, 60 times 3, 180. So 3 times 5 times 6 times 2, 180 and we have 180 different kinds of outfits I can make with these combinations.

Let's look at at a more difficult problem. Once in a while you'll see these and these require an extra step, but you can still do it with no problem. How many different combinations are possible for a seven digit telephone number? Also just an interesting question, I'm kind of curious myself. Well, okay, think about what we did before, we thought about how many choices we had for each option and we multiplied that. Right we have... I'll take 3 skirts, 2 shirts, so how many choices for each and then multiply them. Here we know we have seven different options right? So seven different numbers in our telephone number, one, two, three, four, five, six, seven. And the question is how many choices for each one of those slots for the number? Okay, this is the part where it's harder; you have to think how many choices are available there? Well for each digit of a phone number, ten choices right, you've got zero, one, two, three, four, five, six, seven, eight, nine, that's ten. So how many different combinations are possible for seven digit number? Well ten options for everyone in the slots, so you would have 10 times 10 times 10 etcetera for each of the seven slots, so really 10 to the seventh power. Okay and we if we do that on a calculator, what would that look like? Well, 10 to the seventh is 10,000,000, okay that's answer choice C, perfect. So 10,000,000 different possibilities for a seven digit telephone number. Again we've found the amount of slots that we need to fill right, seven slots for the seven digits and then how many options for each digit, 10 and then we just did 10 times 10 times 10 times 10 times 10 times 10 times 10. That's the amount of total combinations that we have, great.

Next one hit wonder, matrices. Students tend to get really intimidated with these. They look at them maybe it's been a while since you've seen it, maybe you haven't seen this at all. Actually, they're really easy once you know what to do. You've got this funky looking shapes here with some numbers in it. All you need to do is combine them in whatever way they tell you and you're going to combine each number with its corresponding number in the other square. So here, what is A plus B? Okay, so here you want to add A and B and all you do is add each number to the corresponding number. So for example, 2 plus 0 is 2, 3 plus 2 is 5, and you know what, let's first look at the answer choices too and just make sure do we even have to keep going. 2 plus 0 is 2 and actually only one of these even has a 2 here. So 2 plus 0 is 2 but let's just double check. We said 3 plus 2 is 5, that looks great, 0 plus 1, 1 and negative 1 plus 1 is 0. So this is the solution for this matrix problem. So you see, not that complicated at all, nothing to be intimidated about. And once in a while you'll have subtraction and then you would just subtract each relevant part. So that's a matrix problem.