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TrigonometryMediumGraphs of the Other Trigonometric Functions

Graphs of the Other Trigonometric Functions · Medium problem

By how much is the graph of y=2cot⁡(12x+π2)−1y = 2\cot\left(\dfrac{1}{2}x + \dfrac{\pi}{2}\right) - 1 shifted horizontally compared with y=2cot⁡(12x)−1y = 2\cot\left(\dfrac{1}{2}x\right) - 1? Give the signed shift as an exact multiple of π\pi (positive means to the right).