Question

For what values of x is it true that |sin(x)-x| < 0.01?

Answer 1

I have spend 20 min on this,with no results. I went the Taylor expansion of sin(x), and it didn't help. When you get a solution, please post it. FYI, I graphed it, and was surprised. It reminded me how accurate the small angle approximation is.

Answer 2

I looked at the solution to
|sinx -x| = .01 and using Newton's Method found
x = ±.392493378

then testing, I found the above to be true for

-.3925 < x < + .3924

x is in radians

(for sinx - x = .01 my iteration expression was
(xcosx - sinx + .01)/(cosx - 1) )