How do you get rid of the SIN() function to solve for x?

1. r3dxP

0
i have x*sin(x/2) - 18/pi =0
and i need to solve for x..
how in the heck can i get rid of that sin() function? very confused.. any help will be appreicated..!
btw.. i need the answer ASAP! thanks alot guys

2. Fermat

876
Can you use newton's method of approximation ?

3. r3dxP

0
i guess you can, could u explain how i would do that? and give me the answer for x=? thanks

4. Fermat

876
Here's a good description and an example of newton's method of approximation.
You will have to find the initial starting point, x0 -- the firstapproximation -- yourself.

To do so, make up a table of x and f(x) values, where f(x) = x*sin(x/2) - 18/pi.
Use values of x like: pi, 2pi, 3pi, ... until you get a change in the sign of f(x). That means that the curve, f(x), has crossed the x-axis, and therefore has been, at some point, equal to zero between the two x-values that gave the change of sign.

Take half-way between the two x-values as your first approximation, x0. You can get a closer approximation to x0 if you are familiar with interpolation. But that might be a bit of overkill at this point.

5. r3dxP

0
thanks alot. i just figured out that i can just graph it with ti83plus, then go2 calc and use the 'zero' function :) thanks for the help

6. hotvette

931
Even though you have the solution from the TI, here are additional comments that might be useful. Since this function is periodic, it will cross y=0 many times (see thumbnail). Newton's method works extremely well and converges very quickly on the solution, provided the starting guess of the solution is sufficiently close. Another option is bi-section, which is computationally much simpler, but takes longer to converge to the solution. Either method can easily be done w/ Excel.

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Last edited: Oct 17, 2005