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

• Saitama
In summary: It's a decimal value. If you were to graph the two sides, you would see that the graphs intersect at around x = -8.423.That's one of the 7 solutions to your equation. For whatever reason that I don't understand,...It's a decimal value.
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.

## The Attempt at a Solution

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

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

Pranav-Arora said:
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.

Mentallic said:
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.

Pranav-Arora said:
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.

eumyang said:
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})".

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.

#### Attachments

• MS_Math.jpg
53.1 KB · Views: 442

eumyang said:
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?

Pranav-Arora said:
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.

eumyang said:
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..."?

Pranav-Arora said:
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.

eumyang said:
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 like Serena said:
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.

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

## 1. How do I solve 10sin(x)=x?

To solve this equation, you can use a combination of graphs and math software. First, graph both sides of the equation on the same coordinate plane. Then, use the intersection feature on the graphing software to find the x-coordinate(s) where the two graphs intersect. These x-values will be the solutions to the equation.

## 2. Can I solve this equation without using graphs?

Yes, you can also use a numerical method such as the Newton-Raphson method or the bisection method to approximate the solutions to the equation. However, using a graph can provide a visual representation of the solutions and can help to verify the accuracy of the numerical method.

## 3. How many solutions does this equation have?

This equation has an infinite number of solutions. However, when using graphs and math software, you will typically find only a few solutions that fall within the given domain and have a high enough degree of accuracy.

## 4. What is the purpose of using math software to solve this equation?

Using math software allows for a more efficient and accurate way of solving equations. It eliminates the potential for human error and can handle complex equations and functions that may be difficult to solve by hand.

## 5. Can I use any math software to solve this equation?

Yes, there are many math software programs available that can solve equations. Some popular options include Wolfram Alpha, MATLAB, and Maple. You can also use online graphing calculators, which are often free and accessible on any device with internet connection.

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