05.19 Alg2H 10.2-10.5 and csc/sec/tan graphing Quiz Pointers

追加: 2026-05-21

[00:00:00]Ladies and gents, your quiz tomorrow, listen to me. Listen, listen, listen to me, please. Excuse me again. I don't know what's going on with my voice. Your quiz tomorrow is eight questions.

[00:00:14]All right, there's going to be two that are graphing and then six that are matrices. I'm going to tell you exactly what to expect. I highlighted exactly what's going to be on there. This review just has a ton of practice, which is good for you guys to do. But as far as the matrices question go, right, you're absolutely going to have one like I have highlighted here that you're going to have to distribute and subtract.

[00:00:42]When can you add and subtract matrices?

[00:00:46]Dimensions have to be what?

[00:00:48]>> Dimensions have to be the same when you add and subtract.

[00:00:52]>> Say it again.

[00:00:54]>> Is it row by column?

[00:00:55]>> Row by column. Think about it. It's it's row God bless you. By column, think about if you're graphing.

[00:01:04]When you graph, you go left to right, then up and down. Correct? Same exact way. You go left to right, then up and down. So, when you're adding and subtracting, dimensions must be the same, right? So, there's definitely going to be one of those. There will definitely be a multiplication.

[00:01:27]Definitely. definitely definitely be one multiplication. What's the rule for multiplication when you multiply?

[00:01:35]>> It's right here. What has to be the same? The middle has to be the same. If the middle dimensions are the same, then the outside dimensions tell you what your answer will be, what your result is. Right? So, that's two of the questions. Then we go through here and you're going to have one like this one that says, "Determine if B is the inverse of A. Show your work." Guys, when you do this, what do you have to do to show that things are inverses of each other? What do we do?

[00:02:11]>> You have to multiply A* B and you have to multiply B * A.

[00:02:18]You have to do that. You want to end up with the identity matrix both ways.

[00:02:26]Both ways. You need to do it both ways.

[00:02:28]If you do end up with the identity matrix both ways, then your answer is yes. They're inverses. If you don't end up with the identity matrix both ways, the answer is no, they're not. Whether you get the identity matrix or not, you need to do all of the work. You need to multiply them both ways together to prove yes, they are or no, they're not.

[00:02:47]That make do you guys understand that?

[00:02:50]Okay, that's three questions.

[00:02:52]There is going to 100% be a question of find the inverse. How do we do that?

[00:02:58]What are the steps for finding the inverse? First thing we do is find the >> find the determinant. Your determinant is going to be a * d minus b * c. Right?

[00:03:08]Then we come over here. We put the determinant that you got underneath a one.

[00:03:14]And then we have to set up our inverse.

[00:03:16]We switch the places of the majors and the signs of the minors. Everybody remember that? All right. And then you distribute. What happens if you find your determinant to be a zero and then you get one over zero?

[00:03:29]>> Your answer would be no solution, no inverse, something like that.

[00:03:34]Make sense?

[00:03:36]All right. How many is that? Four. You 100% will have a Kramer's rule.

[00:03:42]More than likely it'll be a 2x two because if you could do a 2 x2 then you can do a 3x3 but we don't have 5 hours and the 3x3's are long right so you'll have a Kramer's rule where you find the determinant then you find the d subx the d suby and then you divide and then the last matrix question will be to find the determinant of a 3x3 you know it'll be like let's just do one real quick say 3 1 -2 0 4 1 1 2 -3 How would you find the determinant here? What's my first step?

[00:04:23]>> Recopy. So 3 1 -2 0 4 1. Then we identify which ones?

[00:04:31]>> The major. So top left bottom right.

[00:04:35]We multiply and combine. Correct? So 3 * 4 * -3 what?

[00:04:46]>> Yes, it is 36. Why' I say 24? 36. Okay.

[00:04:49]0 * 2 * -2.

[00:04:52]>> Good. And then 1 * 1 * 1.

[00:04:55]>> Perfect. Minus. We identify the minors now.

[00:05:00]So here, here, and here.

[00:05:03]What's -2 * 4 * 1?8.

[00:05:07]What's 1 * 2 * 3 + 6 3 * 1 * 0.

[00:05:12]So - 36 + 1 -35 minus what's -8 + 6 -2. Guys, what do we have to be so so so care careful with tomorrow? Your signs, right? So easily we could get to this point and you guys tell me that the answer is negative what?

[00:05:30]>> 37.

[00:05:32]Is the answer here 37? No, because this becomes a plus. So, my determinant is actually negative what? 33. All right.

[00:05:39]Those are the six matrix questions you're going to have. Uh, >> it'll just say find the determinant.

[00:05:47]Yep.

[00:05:49]Super super straightforward. Then you're going to have two graphing questions.

[00:05:53]You absolutely will. So, one graphing question that is a tangent what we did yesterday.

[00:06:03]Do tangents are we shifting left and right? No. Are we shifting up and down?

[00:06:08]No. The only shifts we're going to do with tangent is a speed shift where the amplitude is bigger or smaller. It doesn't mean anything to you. What do I need to see? I need to see your amplitude is on your graph. I need to see the direction. Since this is negative, then my snaky thing is negative. I need to see asmmptotes and I need to see x intercepts.

[00:06:34]>> Uhhuh.

[00:06:41]>> This one.

[00:06:44]>> Guys, remember if you have a reciprocal graph either cosecant or seeant. What did I tell you to do first?

[00:06:54]>> Graph graph the original. So this is cosecant. What is your original graph?

[00:06:58]It would be a sign. I would graph the sign graph.

[00:07:02]Then you know that the reciprocal is just the flipped over part, right? Look at I did this one. I added this. If you guys want to take a picture of it, it's on the video that I'm doing right now.

[00:07:12]But this is how I would do a graph that has a reciprocal and a phase shift.

[00:07:17]Right here, go ahead, take a picture first and I'll talk you through it. But the first thing I did, I did this this morning. Notice what I did. I recognize or identified that the secant graph is actually the reciprocal of what?

[00:07:31]Cosine. So I rewrote the equation as y=3 cosine x -<unk> 5. And I graphed that first. I recognize that cosine's going to start where? At the amplitude or at the axis?

[00:07:44]>> Amplitude. All right. And since this is negative, it's going to start at the bottom or at the top.

[00:07:49]>> Bottom. Okay. I also identified my shift. Where did I shift?

[00:07:55]to the right since it's minus it's the opposite of what we think. So we went to the right. So I wrote down my starting point is pi over five. Now guys remember when we shift left and right with these graphs we don't multiply by 1/4 24s 34s 44s. What do we do?

[00:08:10]>> You add pi over two. You also do what?

[00:08:13]Subtract. Right? So that's the hardest part of this is just adding pi over two.

[00:08:18]You got to get a common denominator. All that good stuff. But I found four points to the right. I then subtracted found four points to the left and I graphed in red the -3 cosine graph. Notice I started my starting point was right there at the bottom and I just did my graph really easy. But that's not what I'm what the end result your end result would be your seeant your reciprocal. So where do we draw our asmtotes?

[00:08:51]Where are your asmmptotes drawn?

[00:08:54]>> God bless you. Right, the x intercepts.

[00:08:56]Your asmmptotes have to be on your graph and they're right here. Wherever the x intercept is. Good.

[00:09:04]So, it's real easy for you guys to see.

[00:09:06]I would not try to do all of this in your head. I would put it on paper. Use my color pencils. Whatever you guys need.

[00:09:13]And then to do the reciprocal graph, if you guys listen to the video or anything like that, I told you this is like your hinge point. Do you see how this graph originally is there? Well, the reciprocal one, you just flip it. So that's all we did was just flip. Then I came to here, my hinge point. Instead of going downward in this little area, it flips up. Same thing here. In between these two asmmptotes, there's my hinge point. Instead of this going upwards, what happened to it? It just flipped. It comes down.

[00:09:46]Here's another hinge point. It's always in between the asmtotes. You just flip.

[00:09:51]And then here, it's hard. I know some of you were trying to do the web assign.

[00:09:55]It's hard to pick a graph just by looking at the four of them because they don't have all the stuff drawn. It's very hard to do. So, just take your time. You guys, everyone in here knows how to graph this cosine. We did it already on a test or a quiz. You guys were great at it. So it's just one two extra steps is to just put the asmtotes on and then in each section just flip the graph. That's it. But the quiz is extremely straightforward.

[00:10:20]Didn't throw any curve balls or anything at you. Does anybody have any questions?

[00:10:25]Yeah.

[00:10:25]>> You said one was u >> one will be tangent and the other one will either be seeant or cosecant depending upon what version you guys get.

[00:10:36]>> Yeah. No calculators. The numbers aren't huge. I already worked out all the versions and they're not bad.

[00:10:42]But what is 2 * 3? Six, not five, right?

[00:10:47]Minus a negative becomes a positive.

[00:10:49]Like just take your time. Nobody I've never given extra points for anybody who finishes first, right? Just take your time. Recheck your work and trust yourself. And this is the last thing we have to do, guys. It's so exciting.

[00:11:04]Anything else, you guys? Okay. Is there >> Is it a What is it?