## Precalculus (6th Edition) Blitzer

Step 1. Start from function $y=sin(2x)$ (purple) which has a period of $\pi$ to obtain $y=csc(2x)$ (green) using reciprocal properties. Step 2. Start from $y=csc(2x)$ (green curve), shift the curve $\frac{\pi}{4}$ to the right, and then shift the result up 1 unit to get the red curve for $y=csc(2x-\frac{\pi}{2})+1$