Two sine functions of the form \( y = \sin(x - h_1) \) and \( y = \sin(x - h_2) \) will have the same graph if their arguments (the expressions inside the sine function) differ by a multiple of the sine function's periodicity, \( 2\pi \).
The sine function is periodic with a period of \( 2\pi \), which means that:
\[ \sin(\theta) = \sin(\theta + 2k\pi) \]
for any integer \( k \). This property implies that two sine functions can be equivalent if their phase shifts (in this case, the \( h \) values) differ by a multiple of \( 2\pi \). Therefore, we can say:
\[ x - h_1 = x - h_2 + 2k\pi \]
for some integer \( k \). Simplifying this gives:
\[ h_1 - h_2 = 2k\pi \]
Thus, the two sine functions \( y = \sin(x - h_1) \) and \( y = \sin(x - h_2) \) will have the same graph if:
\[ h_1 - h_2 = 2k\pi \]
for any integer \( k \). In other words, the difference between \( h_1 \) and \( h_2 \) must be a multiple of \( 2\pi \).
In summary, the two sine functions will have the same graph if the values \( h_1 \) and \( h_2 \) are related by:
\[ h_1 = h_2 + 2k\pi \]
for some integer \( k \).