Because y=tan(x+pi/2)=-cotx hence its the graph of cotx only in the opposite direction. The image below show the graphs of cotx (red line) and -cotx (green line)
Tan Graph - GCSE Maths - Steps, Examples & Worksheet
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Tan Graph - GCSE Maths - Steps, Examples & Worksheet
Sketch the graph of y = tan x for: (a) (i) 0° ≤ x ≤ 360° (ii
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Further Trigonometry: Use Graph to Find Solutions to y = tan x
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Tan Graph - GCSE Maths - Steps, Examples & Worksheet
Arctan
Graph of y = tan x Trigonometric functions, Graphing, Function
Table: y = tan x – GeoGebra
