when would two sine functions of the form (y = sin(x - h)) that have different values for (h) have the same…

Brief Explanations:

The sine - function is periodic with period (2\pi). So, if (h_1) and (h_2) differ by (2k\pi) ((k\in\mathbb{Z})), the graphs of (y = \sin(x - h_1)) and (y=\sin(x - h_2)) are the same as the shift is a full - period or multiple of full - periods.

Answer:

Two sine functions (y = \sin(x - h_1)) and (y=\sin(x - h_2)) have the same graph when (h_1 - h_2=2k\pi), where (k\in\mathbb{Z}).