Find all solutions of the equation $\sin x-\frac{6}{x}=0$ for $x\in[0,12\pi]$

Asked Oct 04 '16 at 12:57

Active Oct 04 '16 at 13:23

Viewed 136 times

I need to solve the equation $\sin x-\frac{6}{x}=0$ for $x\in[0,12\pi]$.

I tried substituting $\sin x=\frac{e^{ix}-e^{-ix}}{2i}$ and solving the quadratic but it did not lead to anything.

It has 10 solutions but I do not know how to get the exact values.

edited Oct 04 '16 at 13:23

N. F. Taussig

asked Oct 04 '16 at 12:57

Adit Jain

equations like this usually don't have closed form solutions. you have to refer to numerical or graphical methods – tired Oct 04 '16 at 13:00
You can't, at least in terms of elementary functions. – MPW Oct 04 '16 at 13:00
Here are some numerical results: https://www.wolframalpha.com/input/?i=x*sin(x)-6%3D0 – MrYouMath Oct 04 '16 at 13:04
You'll get 8 solutions, not 10. – Jan Eerland Oct 04 '16 at 13:10
you may notice that the solutions become closer and closer to an integer multiple of $\pi$ as $x$ becomes large. – tired Oct 04 '16 at 13:38

0 Answers0