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Find the all solutions of Ins " equation in the interval [0,23):2cos(z) + v= 0...

Question

Find the all solutions of Ins " equation in the interval [0,23):2cos(z) + v= 0

Find the all solutions of Ins " equation in the interval [0,23): 2cos(z) + v= 0



Answers

Solve each inequality. State the solution set using interval notation when possible. $0.23 x^{2}+6.5 x+4.3<0$

So we're going to find all the solutions on the interval between zero and two pi notice for including zero but we're not including two pi. So the first thing that we can do is we can go ahead and we want to solve for second squared X. Now you could also this is a square minus the square. You can also factor it so that's your choice. But in the end seeking X equals plus or minus one. Now I don't know about you but I think much better and co signs and signs. So I'd like to change my second ex into a one over cosine X. So what I could really do is I can consider that one over Cosine X equals plus or minus one. And then I could take the reciprocal of both sides and of course the reciprocal of one or negative one is still one a negative one. So I'm looking for where X equals um or the co sign of zero equals one or negative one which is zero and pi. And then I don't have to include two pi because we're back to zero there and we don't include it in her interval.

So we're solving this equation. The coastline of X is greater than or equal 2.3 over the interval. So we know our angle is in radiance of 0 to 2 pi. And if we quick think of the sketch of co sign, we know that it has a period of two pi and that the graph has an amplitude of one. And so and co sign starts at a high and let me just kind of mark in here where the hi over twos are and the graph does this and does this and does this and we want to know where it's equal 2.3. So we can see that there are two. Uh we want it to be greater than or equal 2.3. And so we can see that that happens here and that happens here and this 0.3 is not a value that we know right away. So we'll have to use our calculators. So if we find the inverse co sign of 0.3, let's see what that angle is. An inverse co sign of 0.3 tells us that that angle is approximately 1.266 And that would be this angle 1.266 And we know if we add on plus two pion, we would find more angles that would work and that would be the next one down here and next one down here and so on. And the other one we can find very easily by taking the opposite of that angle. So the opposite of that angle is if we had continued the graph this way, this angle is at negative 1.266 So we can see that are one of our solution parts is when x is between zero or from zero all the way up to 1.266 That that will be a solution set for hours because that's where the graph is higher than 0.3. And then now we need to find this angle. So what do we do we take this negative value? So multiply that value in my calculator, times negative one times negative one. So I have this value in my calculator. And if we add on to pie we will find this one plus two pi. And that angle is 5.17 So if we are from 5.17 up to two pi up to two pi, that is our solution set for this uh inequality.

All right, so for this particular problem we are going to determine where the coastline of X. Is greater than or equal 2.3 on the interval from zero to two pi Okay so um to do this particular problem, I am going to use a graphing calculator or demos um in order to solve. So um what I'm going to do is I'm going to type in two equations. The first is that why equals the co sign of X. And the second is that y equals 0.3. Um And then I'm gonna look at some intervals where cosine of X is actually greater than or equal to 0.3. I'm also gonna restrict This so that it only goes from 0 to 2 by okay and Dismas so here we go. So here is my first equation I'm gonna type in Y equals the co sign, relax. And I'm going to do that from zero touch you pie. Mhm. Yeah. And you can see my I really need to kind of change my uh whoa man. I think I made it with blue hair. Oh what I do. Uh huh. There we go. I kinda accidentally dropped in on the whole window instead of the heard that I wanted over here. Oh my goodness. All right, here's what I'm gonna do is I'm gonna change this zero And I'm actually gonna do it three pi just because that we can see a little bit more and then this I'm going to go from negative 1.5 two. Okay, there we go. Now I can see this. So that is my first chunk here. And then I'm also gonna graft flying y equals 0.3. Yeah. So I'm looking for everywhere that My graph is greater than this .3. So you can see that I'm going to write this down um in interval notation. Um So it looks like everywhere from zero. So X equals zero two x equals 1.266. So that's the first part. Okay so I'm going to go from yeah 0 to just at one point. Uh huh. Yeah. 1.266 266. And then also yeah. Um I start again at Uh 5.017. Right. 1 7. All the way to whatever to pious. Okay. And that is the interval. That's my solution. Yeah. Amy right there.

Hello and welcome to this video where we're gonna solve a trigger metric equation and we're gonna find all the solutions from 0 to 2 pi So let's take a look what we have sine squared of X is equal to seven. Now I see something squared. And so my instinct is to take the square root of it. It's going to do that. I'm gonna get second of just X. Is equal to plus or minus the square root of seven. Now this is where it gets tricky. We don't have no values of square to seven and seeking and whatnot. So what we're gonna do is either have to use an inverse function on a calculator. Um some calculators will have a second inverse. Some don't. So for example, let's say you don't have one. Like I'm currently using a scientific calculator. The Fezzan, I need to change this in terms of co sign. And the way that works is co sign and seek and have this relationship where they're sort of um It's the inverse is like the multiple, multiple creative in verses. And so what that means is you will take this part and you put it in the denominator. So plus or -1 over the square root of seven. Now that's not proper algebra. So we're gonna put this into uh rationalized denominator form which is square root of 7/7. Now again co sign, we don't know like you know what co sign or which value of co sign is plus or minus square root of 7/7. So you will use a calculator to figure that out. So we'll go with the calculator, Herbal coastline inverse of the square root of 7/7. And we also do co sign of um universe of negative square 7/7. Make sure that your calculator, is that the radiant mode or it's not gonna work out for you? So cosine inverse of mhm. Square root of 7/7. That's how that works. There you go. That is going to be equal to 1.18. And then if we do the same thing but for negative let's see here. So okay. Alright co sign inverse of Negative Square Root seven. Take that the wrong Okay negative square root. Uh huh. There we go. Finally got it typed incorrectly. Okay and so we do that. That's gonna be 1.958. Now here's the thing. Um And what about A. Three there? Okay. Um This is only part of the answer. So if we think about what it is we've just done co signed as an X. Value. So we found uh part associate. If we were doing co sign of route 7/7 that's gonna be let's just say like right here. So we found this solution and then we do negative square seven we found that solution. But if we want to find this solution and this solution will have to do is we'll go to pi minus these values. So too groups. What I do. All right too Pi -1.183 gives us and so and 5.1001. And actually to be around that better. Uh two pi so two pi -1.958 gives us 4.3- five. So there we go. We have four solutions, and that's how we find them all.


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