Relating phasors to trigonometric equations

A voltage source supplying voltage ${\text{V}}_{\text{S}}={\text{V}}_0\sin (\omega t)$‍ is connected to a circuit. The potential difference across one of the elements is ${\text{V}}_{\text{L}}={\text{V}}_{0\text{L}}\sin (\omega t+\theta )$‍.

The current supplied by the source is ${\text{I}}_{\text{S}}={\text{I}}_0\sin (\omega t+\theta +{\displaystyle \frac{\pi }{2}})$‍.