Here is the graph of the function $12 \sin (100\pi T + \frac{\pi}{6})$. As you can see, the sine wave oscillates with an amplitude of 12 and completes 50 cycles per second, with a phase shift of $\frac{\pi}{6}$.

Would you like to explore more details or have any specific questions?

Here are 5 related questions you might find interesting:

1. How does increasing the frequency affect the graph?
2. What happens if we change the phase shift to $\frac{\pi}{3}$?
3. How would the graph look if the amplitude were doubled?
4. How can we calculate the wavelength for a signal with this frequency?
5. How does the graph change if a cosine function is used instead of sine?

Tip: To visualize the effect of phase shift, compare the sine wave to one without any phase shift to observe how it's displaced.