Hi,
Below is my RL circuit which resistor and inductor are in series and the output waveform is across the inductor.



I'm referring to the phasor diagram to calculate the phase shift value between input and output. The formula i figured out is as below:



Am i in the correct way?

 

Can you specify across which component is the output voltage measured? It is significant.
Why have you assumed that the coil has resistance? Is it mentioned somewhere?

I also assume that L is for load and S is for source.

 

Ok, assuming that the output is across the coil, consider this:

\( V_{out}=I_L \cdot Z_L \\
=\frac{V_S}{Z_{total}} \cdot Z_L\)

The angle of that phasor is the phase shift, which, of course, is dependant on the source frequency.
Please write your effort for us to comment.

(is it dependant or dependand? Which is for persons and which is the adjective?)

 

Aside:

(is it dependant or dependand? Which is for persons and which is the adjective?)

"Your dependant is dependent upon you."

"Dependent" is the adjective, meaning to be reliant upon. "Dependant" is the noun.