The problem states that if the graph of $y = \cos x$ is translated $\frac{\pi}{2}$ units horizontally, it will coincide with the graph of $y = \sin x$. We need to determine the direction of this translation.

Solution:

The translation of $y = \cos x$ to $y = \sin x$ can be achieved by shifting the cosine function to the right. Here's why:

1. Horizontal Shift of Cosine Function: The function $y = \cos x$ can be transformed into $y = \sin x$ by shifting it $\frac{\pi}{2}$ units to the right. This is because:

   • $\cos(x - \frac{\pi}{2}) = \sin x$.

2. Direction of Translation:

   • Translating $\cos x$ to the right by $\frac{\pi}{2}$ units aligns its peaks, valleys, and zero-crossings with those of $\sin x$.

Conclusion:

The correct direction of the translation is to the right.