recovering phase of sine signal from FFT
It makes sense after all: your phase estimate is an estimate of the unknown phase angle $\phi$ minus $\pi/2$, because you're using a sine function. So the phase of the FFT at the appropriate frequency index corresponds to $\phi-\pi/2$. So in your example, $\phi\approx -0.98+\pi/2=0.59$, which is a lot closer to the actual phase. If you used a cosine function, your way of estimating the phase would be correct.