How do you find the exact value of $tan^-1 (-1)$ ?

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Answer 1 · 2017-08-08T18:06:30

$-pi/4 " or " (3pi)/4$

Well, if

$arctan(-1) = theta$

then

$tantheta = -1$

There are two values of $theta$ that satisfy this, according to the unit circle:

![upload.wikimedia.org]( useruploads.socratic.org )

$color(blue)(ulbar(|stackrel(" ")(" "arctan(-1) = -pi/4 " or " (3pi)/4" ")|)$

Answer 2 · 2017-08-08T18:09:50

$tan^-1x=theta, x in RR iff tantheta=x, theta in (-pi/2,pi/2).$
Now, $tan(-pi/4)=-tan(pi/4)=-1, -pi/4 in (-pi/2,pi/2).$

$:. tan^-1 (-1)=-pi/4.$

How do you find the exact value of tan^-1 (-1)tan^-1 (-1)?