How do you graph y=tan(x+90) ?

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)

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Vector set of mathematical function y=tan x and y=cot x. The

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Trigonometry and Life – Chronicles of Calculation

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6.3.1 General Pattern for y = sinx, y = cosx and y = tanx - SPM

Table: y = tan x – GeoGebra

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The graph of y = tan x – GeoGebra