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Show that 31 _ 2 + coS =0 has exactly one real root On the interval [-1,2] Show all work and explain yOur answer very carefully using complete sentences....

Question

Show that 31 _ 2 + coS =0 has exactly one real root On the interval [-1,2] Show all work and explain yOur answer very carefully using complete sentences.

Show that 31 _ 2 + coS =0 has exactly one real root On the interval [-1,2] Show all work and explain yOur answer very carefully using complete sentences.



Answers

Show that the equation has exactly one real root.

$ 2x + \cos x = 0 $

We are going to do problem number 21 and discussion we need to write the value of theta in interval from zero to to buy from the given equation that is 302 cause of theater plus two equals to management. Now we are going to sub strapped two from both sides. So we will be having three under road to cost theatre 300 to cause theater equals tremendous well managed to that. His ministry are dividing 300 or two from both sides. So we will be having caused theta equals 2 -1 by under oath to now we need to understand that at which quadrant cost function is negative. So cause function is negative in second and in third quadrant. Okay, now the value of 3000 cause function is one by on the road to that is the positive one binder wrote to. So that is pi by four. Okay, so to make it in this second and then third quadrant. Okay so we need the value That is theater will be pie manners by by four. This will be in the second cordant And by plus by by four. This will be in the third quadrant. So 32 in this case will leave four by minus by, that is three by by four And in this case poor by blessed fire. That is played by by four. So this is the answer in this case. So that's all. Thank you.

Um, the first thing I would notice in this problems this one minus co sign of X over three and then one plus co sign of X over three. This looks like if you look in your formula sheet, um, the tangent formula breath eight over to and faith does is X over three that's being divided by two. Um, so that's a sentence. Show the tangent of X over six. So if I were doing this problem, um, I would change that To be tangent of X or six plus one equals zero. And you might be saying there and saying, Oh, well, it's a square root. The reason why that actually doesn't matter on this problem is ah, if you were to square root, you know, when you subtract like the square root of negative one, Um, I believe you had All this is the square root. Um, you're still gonna get the same value. So where does Tangent equal? Negative one. Um, there's two places in the fourth quadrant and the second quadrant, and that's at these values for X. That would be pi over four, except, I mean right, three piper for, um, and I'm actually gonna ignore some of these other ones. Um, like this this woman, Because my next step is to multiply both sides by six acquisition because the directions ask it for Okay, so it asked for all real numbers. Um, I mean, assuming that we're in radiance. Um, anyway, this happens for every end pie units, because for tangent, everything's a semicircle way. Eso if I just multiply everything by six there ago that will find the values for X. It'll make this work. So if I distribute that in 18 Piper four is nine pie or two plus six n pi. And what you also want to tell your readers that n is an integer because it repeats every semicircle. So this the interim committing to

You two have a course factory acts in what you won in Miss Diana Tree next must Nico to zero. And because we're looking for a one of a certain set, we need to press with the jewels and fine. And then we want to find the ex their furniture communist and thankfully, Niko. Judy, if I reckon great three you're gonna do And by inventing Bedri business where the end is in danger said is only the social looking for

According to question sine three x sine three x kos Who Wicks Ness Cross off three X Sign Who wigs equals one right now. This can record this and fight into Sino three x bless two weeks, which is simply equals Sino Sino five picks equals one, so this will finally turn into Sino five. IX equals one. Now the period of design person is two pi. So in the interval, zero to buy the only value at which designed function is one a spy upon to. So all the solutions to sign a five x equals one is given by Hynix equals by a corn too. Let's win fight, right? Who are any is any indigenous the solution in the intervals? Wrote poop. I is often by letting n equals violating n equals zero one who see and food so upon putting these corresponding values off and we will get the values off X as fire pointing fire porn who? Nine By appointing 13 by 13 5 corn thin. And finally we will get 17 5 a born pain. So in total, we were getting five friend wells off X with satisfies is to give any question So this will be the final answer


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