Solving 10sin(x)=x: Find # Solutions w/ Graphs & Math Software

[Saitama]

Confused in graphs?

Homework Statement

My teacher gave a question in which he have to find the number of solutions:-
$$10sin(x)=x$$
I solved it using the graphs and i got the number of solutions to be 4.
But when i came back home and tried to do it on Microsoft Mathematics, i found the results to be completely different. Number of solutions came out to be 1.
I think i have used some wrong statement in Microsoft Mathematics. Please someone tell me the correct statement.

Homework Equations

The Attempt at a Solution

 

[eumyang]

I found MORE THAN four solutions, so it's not either 1 or 4.

 

[Saitama]

Oops Sorry! It's 7 but please solve my problem!

 

[Mentallic]

Oops Sorry! It's 7 but please solve my problem!

Is your problem why Microsoft Mathematics gave you just 1 solution or how to find that there are 7 solutions?

The program would've given you the smallest positive value for various reasons.

 

[Saitama]

Is your problem why Microsoft Mathematics gave you just 1 solution or how to find that there are 7 solutions?

The program would've given you the smallest positive value for various reasons.

My problem is Microsoft Mathematics gave me only 1 solution.

 

[eumyang]

My problem is Microsoft Mathematics gave me only 1 solution.

I downloaded the program, and now I see what you mean. I get the same issue. When I type this in the worksheet:
nsolve({10 sin(x) = x},{x})
I only get one solution of x ≈ 0. However, when I graph the two sides, the graphs do intersect 7 times. The only way I could get it to give me all solutions was to limit my range of x values and type the nsolve command 7 times.

For the 2nd solution, I typed this:
nsolve({10 sin(x) = x},{x,-10,-8})
(the bolded indicates that the program should only look at x values between -10 and -8) and I got x ≈ -8.423... I repeat this 5 more times, changing the range of x values (bolded) by looking at the graph each time. Eventually you'll get all 7 solutions. Very tedious. As today was the 1st time I ever used Microsoft Mathematics, maybe someone here who knows more could chime in.

 

[Saitama]

I downloaded the program, and now I see what you mean. I get the same issue. When I type this in the worksheet:
nsolve({10 sin(x) = x},{x})
I only get one solution of x ≈ 0. However, when I graph the two sides, the graphs do intersect 7 times. The only way I could get it to give me all solutions was to limit my range of x values and type the nsolve command 7 times.

For the 2nd solution, I typed this:
nsolve({10 sin(x) = x},{x,-10,-8})
(the bolded indicates that the program should only look at x values between -10 and -8) and I got x ≈ -8.423... I repeat this 5 more times, changing the range of x values (bolded) by looking at the graph each time. Eventually you'll get all 7 solutions. Very tedious. As today was the 1st time I ever used Microsoft Mathematics, maybe someone here who knows more could chime in.

Where to type this nsolve command?
And where you typed this equation "nsolve({10 sin(x) = x},{x,-10,-8})".
Please provide a screenshot.

 

[eumyang]

See attachment. I typed the command in the "Worksheet" tab. Also, on the top, I had already clicked the "Home" tab. Make sure that you are in Radian mode. This is using the latest version, 64-bit.

 

[Saitama]

See attachment. I typed the command in the "Worksheet" tab. Also, on the top, I had already clicked the "Home" tab. Make sure that you are in Radian mode. This is using the latest version, 64-bit.

I got my answer but what does this -10 and -8 denote?

 

[eumyang]

I got my answer but what does this -10 and -8 denote?

Please re-read 1st post (#6 in this thread). If you look at the graph, you will see that, going from left to right, the first time the two graphs intersect is somewhere between x = -10 and x = -8.

The next time the graphs intersect is somewhere between x = -8 and x = -6, so I would type this to find the next solution:
nsolve({10 sin(x) = x},{x,-8,-6})

And so on.

 

[Saitama]

Please re-read 1st post (#6 in this thread). If you look at the graph, you will see that, going from left to right, the first time the two graphs intersect is somewhere between x = -10 and x = -8.

The next time the graphs intersect is somewhere between x = -8 and x = -6, so I would type this to find the next solution:
nsolve({10 sin(x) = x},{x,-8,-6})

And so on.

But what does this mean "x ≈ -8.423..."?

 

[eumyang]

But what does this mean "x ≈ -8.423..."?

That's one of the 7 solutions to your equation. For whatever reason that I don't understand, in MS Mathematics we are not able to get all 7 solutions at once. That's why I said that you'll have to enter the nsolve command 7 times, changing the range of x-values each time, so that you can get all of the solutions.

This command that I wrote previously:
nsolve({10 sin(x) = x},{x,-8,-6})
more or less is telling the program to ONLY look at x-values between -8 and -6 and state the x-value that makes the equation true.

 

[Saitama]

That's one of the 7 solutions to your equation. For whatever reason that I don't understand, in MS Mathematics we are not able to get all 7 solutions at once. That's why I said that you'll have to enter the nsolve command 7 times, changing the range of x-values each time, so that you can get all of the solutions.

This command that I wrote previously:
nsolve({10 sin(x) = x},{x,-8,-6})
more or less is telling the program to ONLY look at x-values between -8 and -6 and state the x-value that makes the equation true.

Thanks for paying attention to this thread!
(I think i need to learn more about this program)

 

[I like Serena]

Are you already aware of Wolfram Alpha?
That one does not give you the misleading surprise that you only get 1 solution, when there are more.

See this link:
http://www.wolframalpha.com/input/?i=10sin+x=x

 

[Saitama]

Are you already aware of Wolfram Alpha?
That one does not give you the misleading surprise that you only get 1 solution, when there are more.

See this link:
http://www.wolframalpha.com/input/?i=10sin+x=x

I know about Wolfram Alpha.