Find All Solutions to the Equation 2cosî¸ Root3 0
6. Find all values of x in the interval [0, 2r] that satisfy the inequality: 2 cosI + 1 > 0. Answer: = € [0, %)u (%,2r] tan T sin I _ COs I sin $ . Answer: I € [o, #) u (5,24] -1 < tanz < 1 Answer: € € [0, #Ju[##Ju [4,20] (a) Find the exact value: sin` -'(1/2) , arctan 1, SCC Auswer: % $ { (6) Find the exact valuc: sin sin(7) , cOs sin 5 cos(sin`'(3/5) ) , sin(2 sin ~'(2/5)). Answer: 2T 5, %, 4 c) Simplify the expression: tan(sin 1) , cos(sin 1). Answer: VI-r
6. Find all values of x in the interval [0, 2r] that satisfy the inequality: 2 cosI + 1 > 0. Answer: = € [0, %)u (%,2r] tan T sin I _ COs I sin $ . Answer: I € [o, #) u (5,24] -1 < tanz < 1 Answer: € € [0, #Ju[##Ju [4,20] (a) Find the exact value: sin` -'(1/2) , arctan 1, SCC Auswer: % $ { (6) Find the exact valuc: sin sin(7) , cOs sin 5 cos(sin`'(3/5) ) , sin(2 sin ~'(2/5)). Answer: 2T 5, %, 4 c) Simplify the expression: tan(sin 1) , cos(sin 1). Answer: VI-r
Solve each equation on the interval $0 \leq \theta<2 \pi$. $$\sin ^{2} \theta=6(\cos (-\theta)+1)$$
We have to solve. Sign Esquire Tater is equal to six multiplied by course or potato plus one. No, this can be written as one minus course. Esquire Tater is equal to six course to top plus six this can Britain has caused disquiet data plus six course Cheetah plus five is according to zero where Trita belongs to approach Interval zero to opening by now. If we fact rise this this can berating at course Tater plus one multiplied by course, Cheetah plus five. This is equal to zero. Now we see that either course cheetah is equal toe minus one or course cheetah is equal to minus five. But the main minimal loop question is minus one. So north or losing from this equities. And now we see that question is equal to minus one Air Tater equal to buy only two means by is the only sort isn't off this equation
So to begin solving this equation, let's use the some two product formula Formula number nine, and this tractor. So this will convert to negative two TEM sign of a plus B. And here, fourth data is our A six. Data is R B. So we have fourth data plus six data. Just 10 data over to time. Sign of a minus bi. So negative to theater. Forgot to tell you over to equals, Sirrah. So just simplifying these factions. Negative to sign. Five data I'm signed of negative. Safe equals zero. So if we divide by two negative to everywhere we get sign of five data I'm sign of negative data equals zero since zero. Divided by negative to still zero. So now, since we have two factors multiply together equaling zero, we can use this, your product property. So we have two possibilities. Another sign of five feta equals zero or sign off. Negative data equal, sirrah. And so now what? We're going to solve each of these on the interval, zero to to high so sign of five. Data equals zero than five. Data well equals zero. Hi. Those are the two places in this interval in which are signed value is zero. So we divide by five to kept data equals zero or pie over five. This is now These are much smaller than two pilots. See if there any additional solutions. So it could also equal to pi three pie for a pie right by six pie etcetera so we can continue getting more solutions. So we get to pie over five three pi over five four pi over five 5/5, which is pie six pi over five seven pi over five eight pi over five nine pi over five and 10 pi over 51 can't include because that is to pipe and we cannot include two pilots as far as we can go. So this is our first set of solutions from our first equation. That's a question over here, so we may have more solutions from the second equation to let's solve this equation. It's a sign of negative fatal equals zero. Well, just reread it down here, So that means that negative data must equal zero or high, or it could equal negative high as well. You could also equal to prior negative two pi. Those probably won't lead to solutions, though in this case, in this specific interval. So dividing by negative one, would you get some additional solutions for data we get? They don't get cool. Zero. If we divide tie by negative one, we get negative pie that's not in the interval. Be need. But if we divide negative pie by negative one, we get pie zero and pie our solutions for us here. So let's go back because zero and pie are actually already included in the set of solutions from earlier. So this set of solutions is thus a complete set of all the solutions to this equation. In the interval, 0 to 2 pi. So this is our final answer.
No, we have a number 71. And of it we need to stop that. You're gonna medication, Give any question and intervals zero toe by. Okay, well, we have cause to Peter. Let's six transport Peter call toe for in zero net. Technical Peter Lesson Topa. So first we need to gonna wear hold the terms, all the terms, either in scientific or cost eater because it is quoted in scientific, so it will be very convenient. You can work it in tow. Ah, the expression off scientist. Only because we have double angle from raw. Of course, Peter. Yes, So it will be using formula was to cater equal to one minus two. Science got data. Cost would hit ableto one minus two transport. Peter it in place science. But just plug in there, Okay? Even just plug in this value over here, it will become one minus two Science Where? Tita bliss. Six cents per tater, Equal to four. That means six minus tool food stance with Peter equal to four. That is for science. Predatory called three. It implies San Square Tita equal to 3/4. So we have scientist ableto bless. Minus under 3/4, Our plus minus under three over to. So, no, you have scientists equal to under 3/2 and Sanpete ableto minus. And the route. Do you want to know if you see the graph of scientific data? It is like this. And if this is Route 3/2, this angle must be by over three. So this thing, this is room 3/2. The single must be by my inspire. A tree that is to buy over three. Okay, little stick minus root 3/2. So if this season minus root 3/2, this anger must be, is it? Bye bye Plus pirates before by over three. And this single must be two by minus by over three, that is fight by over three. Okay, so now we will go ahead with this. You're right. Saying he take will toe sign either by over three. You are fine to buy over three that is hit becomes by over three. And by over three spins neither the values This is by between 0 to 2 pi. So there are only to well use here, will you? Or we can also say that extends Yes, I am. Peter had period of Dubai. So we have. We take well to bye bye. Three plus two. And by and 253 plus to impact these air quote the general situation well, and it indeed it Okay, now, if people again and equal to zero, we've been forgetting what I call toe. Bye bye three. And to pirate tree, which is well inside of a bill by now, if you plug in an equal to one, we get to fire more than Dubai and more than two kinds. So that should be neglected. So we have in this case solution this. And if it look for this, we will be having t tickle toe four by over three and five by over three. And we need toe to empire. Because to empire, the idiot you went by and fight by by three plus two. Empire when we're en belongs toe in teacher. Now we need to kind of a look between zero to pass. So just plug in an equal to zero replicating Tate, I call to for 53 and fight by where three and if you plug in an equal to one. But I will be more than poopers. Don't let it leave it. Okay, so our solutions are on society. Table toe by over three. No pirate. Three for 53 and five by military Deserter Answer. Thank you.
So to solve this equation for theta, let's begin by applying a some to product formula. Formula seven from the section will help us out here. So let's call forth IATA Alfa and six Data Beta. Then we know that sign. Alfa minus sign beta is equal to two time sign of Alfa minus beta. So forth. Ada minus six Data. Oh, too. Times co sign of Alfa plus beta. So in this case, fourth data less six data over to not equal zero. So then, if we divide by two on both sides, the two bets eliminated here and zero divided by two is still zero, so we'll still be equal to zero. Then let's simplify the expressions inside of signing co sign so forth. Beta minus six. Data is negative. Two fada to dividing by two that is naked of Fada. And here adding together for data and six data. We get 10 data writing by two. So we get co sign of five feet. All right, so now we have to products that multiplied together equals zero so we can apply the zero product property. We have two possibilities. Either sign of negative Fada equals zero. Oh, co sign of fact data equals era, and suddenly they can both be zero as well. So now we're going to solve each of these separate equations, and we want to keep getting solutions from 0 to 2 pi. So if sign of negative data equals zero, the naked of data must be equal to negative two pi or negative pie or zero or pie or two pi All these places where sign of these ankles equals zero. So then dividing by negative one, we get faded, equals, do you pi pi zero negative pie. Negative two pi it, sire. So we only want to take the values that are in between zero and two pi and we're not going to be including two pi. So the values that fit that rpai and zero so we have fada equals zero or data equals pi. So these are our first solutions. We're not done, though, as we make more solutions from the second part, co sign five beta equals zero. So let's all that now. So we need to list all the places where we have a co sign value of zero. So this occurs at pi over two three pi over two five high over to etcetera. So all these places, these odd intervals of high over to So let's divide by five at then will list all of the solutions until we got to two pi. So dividing by five we get Fada equals pi Over 10 three pie over 10 Fifi over 10 which is high over to seven pi over 10 nine a pie over 10 11 pi over 10. 13 pi over 10. 15 pi over 10 on. We could reduce that. She's three pi over two 17 pi over 10 19 pie over 10 and will stop there as anymore And we would get above two pi so we have to stop here. So this is our list of solutions. And so Tikrit a complete list will add in zero and pie from earlier. So also zero and high because they want to have the complete list of all solutions from both pieces of this equation. So we have this very large box of all of these solutions. So each of the is, well, Syria. That's the solution to this equation. So this here is our final answer
5 answers
Subtract 20 from each item in the given sample and compute the mean and standard deviation of the new sample50, 37, 39, 50, 39, 49, 24The mean of the new sample is (Simplify your answer: Type an integer or decimal rounded to the nearest hundredth as needed:)
Subtract 20 from each item in the given sample and compute the mean and standard deviation of the new sample 50, 37, 39, 50, 39, 49, 24 The mean of the new sample is (Simplify your answer: Type an integer or decimal rounded to the nearest hundredth as needed:)...
5 answers
IQR = Queatogy BB one decimal place. the 10 Previous fve of 25 (1 22,28,19,2,3,21, 30 1 (Azoiher summar MDD = and find the 2 interquartiRound the answers to1 Apue
IQR = Queatogy BB one decimal place. the 10 Previous fve of 25 (1 22,28,19,2,3,21, 30 1 (Azoiher summar MDD = and find the 2 interquarti Round the answers to 1 A pue...
Find All Solutions to the Equation 2cosî¸ Root3 0
Source: https://itprospt.com/num/859238/6-find-all-values-of-x-in-the-interval-0-2r-that-satisfy