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- Apr 14, 2013

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I have calculated an approximation to $\frac{\pi}{2}$ using Newton's method on $f(x)=\cos (x)$ with starting value $1$. After 2 iterations we get $1,5707$.

Which conditions does the starting point has to satisfy so that the convergence of the sequence of the newton iterations to $\frac{\pi}{2}$ is guaranteed?