Answer
True.
Work Step by Step
Please note that the graph of $y=A \cos (Bx-C)$ has phase shift $\frac{C}{B}$. So the graph of $y=\cos \left (2x- \frac{\pi }{2} \right )$ has phase shift $\frac{\frac{\pi }{2}}{2}=\frac{\pi }{4}$.
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