Now I need some math help...

audiobliss

I'm doing my calculus homework...and one (well, a few....but this one in particular) of the problems has me stumped.

x^2 = sin(x)

I'm supposed to find all the solutions.



To be perfectly honest, my mind has just gone blank and I can't think of what to do, seeing as how I don't have a 'y'.

Any help would be appreciated!

audiobliss

Ok; I really would appreciate some help! LOL

trubluluc

....the hieroglyphic sign for tequila?

audiobliss

Beats me. I've never been too keen on foreign languages.

gatemplin

x=o is the only solution that I can see. If I'm wrong I will cry.

audiobliss

Ok. I appreciate the answer. But how in the world did you go about it?

audiobliss

This is an odd problem, so I have the answer in the back of the book. It says the answer is (0,0.88).

gatemplin

Well, first step is to simplify. The equation cannot be simplified as far as I can tell.

Now the only value that will make the equation true is the trivial solution of 0.

audiobliss

Here's another problem I'm doing.

For what values of x is it true that abs(sinx - x) < 0.1?

I graphed it and came up with (-0.85, 0.85), and since this is an odd question, I checked it and I got it right. However, shouldn't I be able to do it algebraicly? IE without graphing it?

Thanks!

audiobliss

gatemplin wrote:

Well, first step is to simplify. The equation cannot be simplified as far as I can tell.

Now the only value that will make the equation true is the trivial solution of 0.

I see. I'm not sure if it can be simplified, either. You can come up with x = sqrt(sinx) , but I don't know where to go from there. Maybe it is simplified.

gatemplin

I dont think you can solve it algebraically.

Hopefully this isn't a case of the blind leading the blind. My average in HS for math was 92% though.

audiobliss

Well, I'd hafta say 92 isn't bad. And I'm inclined to agree that you can't do it algebraically. We'll see, I reckon.

audiobliss

Thanks for your help, gatemplin! Much appreciated! I'm assuming you're in college? What math are you/have you/will you have to take?

gatemplin

No problem. I like math but I'm not the greatest at it, just a good student.

I start a five-year mechanical engineering program at the University of Waterloo next week. It's one of the best technical schools in NA. They have some really cool programs like systems design engineering, nanotech eng and mechatronics eng. I would've liked to take one of those but I couldn't make up my mind.

I have taken high school calculus, algebra and geometry, and discrete math.

Where are you planning to go to college and what for?

bobman1235

With all of the Calculus I was subjected to in college, I REALLY feel lik eI should be able to solve that in, like, my head, but... it's just not happenin.

Sometimes graphing really is the best solution, if not the only one. No shame in using it.

audiobliss

Sounds like a fun 5 years you're looking at! I really like math, too; it's my favorite subject. I've been homeschooled from 1st grade on through til now, so when I went to Forsyth Technical Community College to sign up for some classes this summer, they put me in College Algebra. I actually wasn't upset about it at the time, because that summer was going to be a transition from homeschool (with one student) to a 'real' school environment, so I thought it'd be alright to take an easier class and take a summer to adjust. And I guess it turned out to be good, because I met another high school senior who was doing dual-enrollment, and I really liked my instructor and have developed somewhat of a friendship with him. I finished the course with an average of 111.

After that class, we (me, Mom, advisor) were trying to figure out what math I should take next. They said I had to have trig and then take pre-calc, and I had only had HS Pre-Calc. I had looked at the Trig and Pre-Calc books at FTCC and had decided I could skip trig. So, they had me take a college-level math placement test to see what I should go into next. I took that and made a 113 (out of 121, I believe), so they said I should go straight into Calculus 1. Now I'm mad that I took College Algebra during the summer when I could have taken Pre-Calculus and not missed anything. Oh well, I'll just hafta study more for Calculus.

I'll take classes at FTCC next year too, and then transfer to a 4-year college as a junior. Where? I'm looking at Harding University in Searcy, Arkansas (a Christian college) as well as a few public colleges. I'm currently looking at something in the business field, accounting, nurse practitioner, physicians assistant, something in computers, etc. Basically you could say I have no clue. LOL I don't really want to be stuck behind a computer all day (accounting). Not sure I want to cut on people all day, look at/work with bizarre/gross situations (PA, NP). However, I see no down side to working with computers. I could get passionate about that. Can't seem to say that about anything else (besides cars...if I could make a good livin' working with cars...that'd be heaven!!).

I dunno. I just hope I get it figured out soon enough.

I think I just told you a lot more than you wanted to know, lol. But, I said it anyways.

audiobliss

bobman1235 wrote:

Sometimes graphing really is the best solution, if not the only one. No shame in using it.

I've certainly been told that enough in classes. However, I'd rather 'work with the numbers'. Much more concrete, logical, systematic to me. Much more familiar. All well. It's good to be able to do things multiple ways and even incorporate them.

How far did you go with calculus? Why? What did you major in? What are you doing now? (If I may ask...)

gatemplin

audiobliss wrote:

I took that and made a 113 (out of 121, I believe)

What kind of marking system are you yankees on? Everything up here is just out of 100.

audiobliss wrote:

I think I just told you a lot more than you wanted to know, lol. But, I said it anyways.

Not at all. It can take a while before you know what you want to do. If you like what you do, you can be successful in any field.

audiobliss

:eek: :eek: :eek:
YANKEE?!?!?!?! You called me a yankee?! Them's fightin' werds, man!! How far north do you think NC is?

[/RANT]


As for the grading system, I don't know. That '121' stuff, though, just goes for the placement test. All the actual classes and everything are out of a hundred. 100 - 93 is A. We're on the 7-point scale.

HBombToo

gatemplin wrote:

Well, first step is to simplify. The equation cannot be simplified as far as I can tell.

Now the only value that will make the equation true is the trivial solution of 0.

are you sure??? I know its been about 20 years but could you apply the Pythagorus identity to replace sin(x) then solve?

I'll have to get out some books later but I'm just too darned pooped right know.

HBomb

spwuinmk67

Last year, I could've given you that answer in like 10 seconds, now I'm just dumb-founded. And it's too late to go looking for my old calc notes. It can be simplified and solved algebraicly, just I can't remember how at the moment. One a second look at it, change it from x^2=sin(x), to x= square root of sin(x), which makes that your Y. That's as much as I can think of now, by the time I sign off and get in bed, I'm sure I'll remember a little more. If not, I'll look for those notes, I had AP-Calc in Hs, and have the college credits for it too, started calc 2, then left the college.

audiobliss

Wait a minute. So you're saying that if I isolate the x in x^2 by taking the square root of both sides resulting in x=squrt(sinx), the x on the left 'becomes' my y?

spwuinmk67

Let me try this again, now that I slept a little. x^2=sin(x)
x^2-sin(x)=y, because Y is a function of X. From there, I think that you substitute that in for the Y, so it winds up being x^2-sin(x)=x^2-sin(x) and then you have to get all the X's on the same side, and solve for x that way, then input that answer into x^2-sin(x)=Y, and get your answer for Y.

Just kinda ignore my first post.

bobman1235

Why would you want a y? The way to solve most problems algrebraically is to get as FEW (read, 1) variables as possible. Why substitute in a y?

X^2 - sin(x) = 0 is a perfectly valid equation. I can't really remember how to SOLVE it, but puttin ga "y" in place of zero gets you exactly nothing, unless you're trying to solve by graphing, in which case you just find where y=0 on the graph of y=x^2 - sin(x).

This is why (to me) it's easier to solve with graphing - it may be POSSIBLE via algebra, but it's two seconds on a graphing calculator.

Also, someone mentioned square-rooting both sides - careful with that, you have to have a "plus and minus" case if you do that ((sqrt(x^2)) = +/- x., not just x).

Good luck man.

billbillw

audiobliss wrote:

:eek: :eek: :eek:
YANKEE?!?!?!?! You called me a yankee?! Them's fightin' werds, man!! How far north do you think NC is?

[/RANT]


As for the grading system, I don't know. That '121' stuff, though, just goes for the placement test. All the actual classes and everything are out of a hundred. 100 - 93 is A. We're on the 7-point scale.

He's Canook. Go easy. To them, everyone in the states is a Yank.

gatemplin

billbillw wrote:

He's Canook. Go easy. To them, everyone in the states is a Yank.

Exactly

Hey Audiobliss,

Let us know what you teacher says about the answers.

caseymou

I've been out of the math scene for lots'o'years but how's about this:

x^2=sin(x)
x^2-sin(x)=0
x(x-sin(1))=0
solve for sin(1) and insert the resulting number
resdistribute the x term for something like this:
x^2-?????x+0
(x+?)(x-?)
solve for the 2 possible x values
I don't have a calculator so I can't solve completely. Try it out.

bobman1235

caseymou wrote:

I've been out of the math scene for lots'o'years but how's about this:

x^2=sin(x)
x^2-sin(x)=0
x(x-sin(1))=0
solve for sin(1) and insert the resulting number
resdistribute the x term for something like this:
x^2-?????x+0
(x+?)(x-?)
solve for the 2 possible x values
I don't have a calculator so I can't solve completely. Try it out.

Wait : sin(x)/x doesn't equal sin(1). Does it? I don't think so. Maybe the limit as x-> infinity or something, but not just sin(x)/x. SO you can't factor out X as you do in step 3.

spwuinmk67

bobman1235 wrote:

Why would you want a y? The way to solve most problems algrebraically is to get as FEW (read, 1) variables as possible. Why substitute in a y?

Because the correct answer in his book is (0,0.88), which is a cordinate, which would need both an X and a Y, where X=0 and y=0.88. Y is simply a function of X, can also be called f(x) in some books. By doing what I had writen, you can solve for x, and then subsitute that in the Y= equation, and get the other portion of your answer.

gatemplin

I think we're all a little rusty.

bobman1235 wrote:

Wait : sin(x)/x doesn't equal sin(1). Does it?

Nope, cant factor out x or divide it out.

Because the correct answer in his book is (0,0.88), which is a cordinate

Maybe not, it could also be an interval, or a set of solutions for x, although that is not the correct notation for either.

By doing what I had writen, you can solve for x, and then subsitute that in the Y= equation, and get the other portion of your answer.

I think you're onto something though. Maybe you made an algebraic mistake.

if
x^2-sin(x)=Y

and
x^2=sin(x)
x^2-sin(x)=0

then
Y=0
not 0.88

spwuinmk67

Well it's (X,Y) so x=0 and y=0.88, no?

If using your logic that y=0, solve that equation for x, using y=0, and see what you get. I'm too tired and rusty to do it right now.