How do you find the inverse of $y = Arctan(x+pi/2)$ ?

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Answer 1 · 2018-04-03T18:18:18

$f^-1(x)=tan(x)-pi/2$

To find the inverse we need to express $x$ as a function of $y$

$y=arctan(x+pi/2)$

$tan(y)=tan(tarctan(x+pi/2))=x+pi/2$

$tany-pi/2=x$

Substituting:

$y=x$

$tan(x)-pi/2=y$

$f^-1(x)=tan(x)-pi/2$

How do you find the inverse of y = Arctan(x+pi/2)y = Arctan(x+pi/2)?