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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tikz pgf - Plotting one period of f(x)=tan x with the vertical

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The graph of y= tan x° is translated to give the graph y = g(x

Trigonometric Functions