Solving 10 Sin x = -x: Tips & Ideas

In summary, The conversation is about solving the equation 10 sin x = -x. The individual is asking for tips to solve the equation and mentions running out of ideas. Another person suggests using Newton's method to find solutions, and mentions that there are 3 roots in the equation. The individual asks for clarification about Newton's method and finding intercepts between trig and non-vertical/non-horizontal functions. The conversation ends with someone providing a solution with 5 possible solutions.
  • #1
kelvintc
38
0
10 sin x = -x
can anyone give me tips how to solve this equation?
i run out of ideas even to transform this equation to another form.. sigh sigh

thanks...
 
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  • #2
It seems you have a transcendental equation0--i don't think those are solvable, unless you know how to find intercepts between trig and non-vertical/non-horizontal functions.
 
  • #3
x=0

Or do you want more solutions? Then look up Newton's method.
 
  • #4
there are 3 roots in this equation. 0 is the obvious one, the other two needs to estimate by computer.
 
  • #5
oh ... thanks...
p/s : (1) what's Newton method?
(2) find intercepts between trig and non-vertical/non-horizontal functions ?

i not yet learn both also and my textbook is doesnot contain Newton's method also.. i will try to find it out...
my friend told me use 'trials and errors' method, is it applicable ?
thanks
 
  • #6
Newton's method is a clever way of correcting your guess by using the deviation. But you need to know some calculus, and I don't think you know any. In any case, if x_n is your n^th trial, then you find your next trial as follows:
[tex]x_{n+1}=x_n-{10\sin x_n+x_n\over 10\cos x_n +1}[/tex]
Of corse, with more than one root to 10sin x+x=0, you'll need an appropriate initial guess or you'll just keep going back to a known solution like x=0.
 
  • #7
here are the 5 solutions to 50 digits...
0
+/- 3.49906381990775821737274462727340586713040476067
+/- 5.67920779631440367042018458778408009777615397061
 
  • #8
oh .. thanks a lot ... :)
 

1. What is the first step in solving 10 Sin x = -x?

The first step in solving this equation is to isolate the sine term by adding x to both sides of the equation, resulting in 10 Sin x + x = 0.

2. Can I use a calculator to solve this equation?

Yes, you can use a calculator to find the numerical solutions for this equation. However, it is important to note that calculators may not give you the exact solutions, so it is recommended to also use algebraic methods to verify your answers.

3. How do I know if my solutions are correct?

To check if your solutions are correct, you can substitute them back into the original equation and see if it satisfies the equation. If it does, then your solution is correct.

4. Are there any special angles that can help me solve this equation?

Yes, there are special angles that can help you solve this equation. For example, the solutions for this equation will involve the values of x that make the sine function equal to 0, 1, or -1. These values correspond to the special angles of 0 degrees, 90 degrees, and 270 degrees, respectively.

5. Are there any other methods to solve this equation?

Yes, there are other methods to solve this equation, such as using the unit circle or the double angle formula for sine. You can also use graphing techniques to visualize the solutions or use trigonometric identities to simplify the equation.

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