Answer
See graph and explanations.
Work Step by Step
Step 1. Start from function $y=cos(x)$ (purple) which has a period of $2\pi$ to obtain $y=sec(x)$ (not shown to avoid mixing with the final result) in the interval of $[0,2\pi]$ using reciprocal properties.
Step 2. Start from $y=sec(x)$ and reflect the curve with respect to the y-axis to get the red curve for $y=sec|x|$
