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

r3dxP

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

Fermat

Can you use newton's method of approximation ?

r3dxP

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

Fermat

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.

r3dxP

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

hotvette

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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