To find the maximum value of the function \( j(x) = -87 \sin x \), we need to consider the range of the sine function, which varies between -1 and 1.
The sine function reaches its maximum value of 1. Therefore, the minimum value of \( -87 \sin x \) occurs when \( \sin x = 1 \): \[ j(x) = -87 \cdot 1 = -87 \]
Conversely, the maximum value of \( -87 \sin x \) occurs when \( \sin x = -1 \): \[ j(x) = -87 \cdot (-1) = 87 \]
Thus, the maximum value of \( j(x) \) is: \[ \boxed{87} \]
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