[0/1 Points]DETAILSPREVIOUS ANSWERSMcKTRIG8 6.2.007_Solve the equation for 0 If 0o < 0 < 3600_ (Enter your answers as comma-scparated list: ) V3 csc 0 + 9 =24...

solve each equation on the interval $[0,2 \pi) .$ $$ 10 \cos ^{2} x+3 \sin x-9=0 $$

Um So when you're looking at your pathetic and identities, um, you're looking for the coast. Second squared data minus one is a to co change in squared. If they now our problem uses X. So where there is a co change, it squared. I'm gonna replace with co ck in squared minus one. Um, and it starts with co change in squared. Um, change colors because everything else is, you know, minus three co seeking with X, um minus three is equal to zero. And then from here, you can just simplify, like, inedible on minus serious negative four. I believe this is fact herbal, because factors of 41 and four yeah, one minus four is negative. Three. So we have co Seacon of X plus one and co sicken of X. Um, minus four. So that tells you that co seeking of X equal negative one or co second of actually equal positive four. Now we don't have a button in the calculator for co seeking. So that's a reciprocal sign. How the reciprocal of negative one is still negative one, but it makes more sense when I get to this one there is typical for is 1/4. Now we know where this one is on the unit circle Horse that the Y coordinate is negative one. I'm going to change color side of that. That's down here, uh, at 270 degrees. So that's the easy answer. The more difficult answer is this one where you have to do in verse sign because it's not on the unit circle. Make sure you're in degree mode on your calculator, and then, as you type it in, use its second signed 1/4 and they give you one answer, which is 14.48 rounded to two decimal places. Degrees. Um, now that's not the only correct answer, because Sinus also positive in the second quadrant. But this 14.4 is the same as this 14.4. So what you have to do is imagine going 180 degrees a semi circle and then backtracking. So that's 180 minus that 14.48 And when I do that oops, wrong. But my last answer for exit 165.52 degrees

We need to sell the following to damage a good question. You have three sine of X minus by plus co second. Okay. She cost zero. And our domain is from zero. The 360. So um, you can rewrite the function. I'm replace gossiping by one over son. So that would give us three sign of eggs minus five plus one over sine of X. Is the call to zero. It multiply both sides by sign. Giving us to re sign squared of x minus five sine of X plus one is zero. And now at this point we need to use the quadratic formula to find sign. So doing so will give us minus B. 05 plus minus peace accord which is 25 minus four is C. Or minus 12. All divided by two. Hey, just six. So that would give us five plus minus quarter of 13 over six. Which are gonna give us the following solutions for for this part. You need to get your calculators and get the number if you do so you're gonna get in order the air point two 32 and one point or three. So, can this be a solution for son of ex? Yeah, it can is in the range. But how about this? That's bigger than one is out of range. So they can just cross it up and not be bothered by it anymore. Now let's find our solutions for sign. Is he a call to 0.232 to do so let's take the tiny verse of course, Sign universe. Uh going to 32 would give us one solution. Let's look at what does that mean on the unit circle. That's my universe. Is gonna give us a solution over here. But there is another solution over here that we're not finding but you're inside of him. There's only this one. It's going to be equal true 180 minus. That's kind of members. All right, So let's use our calculators to calculate the sign universe and make sure you know how to do your sign in verse on your calculators. The first one I'm going to get 13.4 degrees. And for the second solution, you're gonna get 166. Find six degrees. So these are our solution.

Hello and welcome to this video where we're going to solve and find all solutions from 0-2 pi for the following equation. Co speaking of two X -9 is equal to zero. The first thing we're gonna want to do here is add nine to both sides. So that way I can I can kind of see what I'm looking at here. And so I have co 2nd of two X is equal to nine. Now what I'm going to do is think about what this actually is. So some calculators will have an inverse function for costa rica. And if so you can use it. Um But I'm just using an old fashioned scientific calculator. Mine doesn't have it. So what can I do? Well remember that there's this relationship here sign as it's huge. one over sine of X is equal to co second of X. And so what that means is that we can take we can change this coast seeking of two X and make it um or we'll we'll be Sign of two X is equal to 1 9th. We just take the reciprocal there and that tells us what it has to be. Now I can use inverse trig functions sine inverse of both sides To figure out what I have here. And so two x is gonna equal the sine inverse of 19. And then what I can do with this is divide both sides by two and I'll figure out what X has to be. And so let me do that. Let's go sign inverse of one divided by nine figure what that is. And then divide that by two. And I get X two equals zero point 05567. Give or take a clean that up a little bit 67. There we go. Now let's think about what that means on the unit circle, that means I'm if I want to buy value of about 1/9 I'm not going all that far here, I'm barely moving up my circle here. Um and then I'll have a really small by value. Now, I'll probably have another small by value right here. And the way I find this is I take that value whatever it or I go to pi minus whatever that value is. So I'm gonna go to Pie two pi minus My answer and that's gonna give me 6.2275 give or take. And so those are the two solutions from 0 to 2 pi that would give me a co seeking value of uh nine if I were to times it by two first

Okay, so this time we got coast seeking of X plus two times CO Speaking of X minus, covered up to let's go to zero again, we got to turns multiplying to be make a zero. That means either this is equal to zero or this is equal to zero. Notice that they can't both be simultaneously zero at once. So we're gonna have two distinct solutions. Coast taken X is equal to negative too, or is able to positive scribble, too. Of course, we're not done yet. We need to figure out what X is rather than what cosi gonna excesses. So if co Sagan of X is equal to negative two, then sign of X is equal to negative one half, which then tells us if we look at the graph for sign of X, there's going to two different solutions for it. One of them is going to be here at seven pi over six. The other will be here at 11 pi over six. Now, for the other half, which tells us that Cose Eakins of X is he got to square root of two that tells us ah, sign of X is equal to one over square root of two, otherwise known as scribbled up two divided by two. We know that this happens also in two spots over here and over here here, it's gonna be pi over four together will be a three pi over four. So there we go. Those there are four solutions pie before three pi over four seven pi over six and 11. Pi over six, over. Done.