Solve the following question.
$$\begin{align} \\\sqrt{3}x-\cos 2x=0\\ \end{align}$$
I have no idea how to solve the above question with x inside and outside the cos.Since I have to sketch the graph of the (1)equation[0, $\pi $], if I do not know the value of x when y=0, I cannot sketch it properly.
How can I deal with this problem?
Thank you for your attention.
$\endgroup$ 23 Answers
$\begingroup$Newton's method looks like it will work here.
Start with a rough answer: $x_0 = 0.5$
After that, $x_{n+1}=x_n-f(x_n)/f\,'(x_n)$
The solutions to $\cos x = ax$ do not in general have nice closed-form expressions as functions of $a$.
So unless $a=\sqrt3$ is somehow an exceptional case (which doesn't look likely), the best you can do is to approximate the solution numerically, such as with Newton's method as Michael suggests.
$\endgroup$ $\begingroup$As Michael said, use Newton's method. Since your function is well behaved, start for example at x=0. The first iterate will be 0.57735, the next 0.410054, the next 0.40126, the next 0.40123 and so on
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