how can I analyze a basic sine wave for its frequency phase and amplitude at a particular point in time in matlab
If your the unknown signal $x(n)$ is modeled as:
$$x(n)=A \sin(2 \pi f n+ \phi)+w(n)$$
and you want to estimate $A$,$f$,and $\phi$ accurately, you can use least square estimation. Unfortunately the cost function is nonlinear. You can use nonlinear least square in MATLAB to find the parameters as follows:

Make a cost function: 

f=@(A,f,phi) x[n]-A sin(2*pi*  f *n+ phi)


and use 

p0=[A0,f0,phi0];

p = lsqnonlin(f,p0);  


to find the unknown parameters.
Note that the optimizer will have a hard time finding $f$ as the problem is not convex. So it is best if you can give an initial estimate of frequency by using a method like fft.

If the frequency is known then the problem can be converted to a linear estimation as:
$$x(n)=A \sin(2 \pi f n+ \phi)+w(n)$$
$$=A \sin(2 \pi f n) \cos (\phi) +A \cos(2 \pi f n) \sin (\phi)+w(n)$$
$$=p_1 S[n] +p_2 C[n]+w(n),$$
where $p_1=A \cos(\phi)$ and $p_2=A \sin(\phi)$ are unknown parameters, and $S[n]$ and $C[n]$ are known.