The function \( f(x) = \sin x \) has a minimum value of -1. When this function is translated up 6 units, the new function can be represented as:
\[ f(x) = \sin x + 6 \]
To find the minimum y value of the translated function, we add 6 to the original minimum value:
\[ \text{Minimum y value} = -1 + 6 = 5 \]
Thus, the minimum y value after the translation is:
\[ \text{Minimum is located at } y = 5. \]
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