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.

Explore the graph of the sine function 12sin(100πT + π/6) which oscillates with an amplitude of 12, a frequency of 50 Hz, and a phase shift of π/6. This problem covers key trigonometric concepts suitable for students in Grades 10-12.

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