Answer
See graph and explanations.
Work Step by Step
Step 1. As $sec(2\pi x)=\frac{1}{cos(2\pi x)}$, we can use the original function $y=\frac{1}{2}cos(2\pi x)$to obtain the reciprocal function $y=\frac{1}{2}sec(2\pi x)$.
Step 2. The original function has zeros at $x=\pm \frac{1}{4},\pm \frac{3}{4}, ...$ which become vertical asymptotes of the new function.
Step 3. Using the reciprocal property, we can obtain the new function $y=\frac{1}{2}sec(2\pi x)$ shown as the red curves in the figure.
