Solve for $x$. $8x-4 \sin(2x)=\pi$

Question

Please help me I can't seem to solve this equation. I tried isolating for theta but couldn't figure out how to because there was one in the sine function and one by itself. Please help. I'm studying for an exam tomorrow

Answer 1

We have: $$8x-4\sin(2x)=\pi$$ Rearranging we get: $$x=\frac\pi8+\frac12\sin(2x)$$

We can then approximate the solution using: $$x_{n+1}=\frac\pi8+\frac12\sin(2x_n), x_0=1$$ To get the approximate solution of $x\approx0.8831701433$.