Solving 10 Sin x = -x: Tips & Ideas

[kelvintc]

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...

 

[bomba923]

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.

 

[krab]

x=0

Or do you want more solutions? Then look up Newton's method.

 

[vincentchan]

there are 3 roots in this equation. 0 is the obvious one, the other two needs to estimate by computer.

 

[kelvintc]

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

 

[krab]

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:
x_{n+1}=x_n-{10\sin x_n+x_n\over 10\cos x_n +1}
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.

 

[krab]

here are the 5 solutions to 50 digits...
0
+/- 3.49906381990775821737274462727340586713040476067
+/- 5.67920779631440367042018458778408009777615397061

 

[kelvintc]

oh .. thanks a lot ... :)