Math CentralQuandaries & Queries


Question from chanmy, a student:

please help me to sole this equation x - 2 Sin[x] = 0,thank you

Hi Chanmy,

Since $\sin[0] = 0, x = 0$ is a solution to $x - 2 \sin[x] = 0.$ Are there any other solutions? To answer this I would think of $x - 2 \sin[x] = 0$ as $x = 2 \sin[x]$ and plot $y = x$ and $y = 2 \sin[x]$ on the same plot and look to see where they intersect. If you do so you will see a number $a$ so that $x = a$ and $x = -a$ are solutions to $x - 2 \sin[x] = 0.$ You can use the graphs to approximate the value of $a$ or you can use an approximation technique such as Newton's Method.


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