Find the coefficient of an AR-model

How can I infer the coefficients for an AR(2) model given an autocorrelation plot?

What I have tried so far: I can see this a cos-wave of 0.4 Hz, and then i find the values for each step $(1, 0.9211, 0.6967, 0.3624)$. Since it is an AR(2) model I have to find to coefficients ($a$ and $b$). Then I can solve two equations with two unknowns. So $a$ is $-0.9991$ and $b$ is $1.8141$. Is that the correct approach? And is it even the correct coefficients?

Given that you know the autocorrelation function, you can use the Yule-Walker equations for a generic AR model of order $p$. As you are interested in the case $p=2$, there's no need to complicate things that much.
$$a=\frac{r_1(1-r_2)}{1-r_1^2}$$
$$b=\frac{r_2-r_1^2}{1-r_1^2}$$
where $r_i$ are the coefficients corresponding to the autocorrelation function.