#1
Oct1705, 04:22 AM

P: n/a

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
Oct1705, 04:41 AM

HW Helper
P: 879

Can you use newton's method of approximation ?



#3
Oct1705, 04:42 AM

P: n/a

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




#4
Oct1705, 05:08 AM

HW Helper
P: 879

how do you get rid of the SIN() function to solve for x?You will have to find the initial starting point, x_{0}  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 xaxis, and therefore has been, at some point, equal to zero between the two xvalues that gave the change of sign. Take halfway between the two xvalues as your first approximation, x_{0}. You can get a closer approximation to x_{0} if you are familiar with interpolation. But that might be a bit of overkill at this point. 


#5
Oct1705, 06:31 AM

P: n/a

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
Oct1705, 01:47 PM

HW Helper
P: 930

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 bisection, 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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