We know that the range of arc-cotangent function is $(0,π)$
and we I calculate the value of $cot^{-1}(-1)$ by a calculator, I get ($-π/4$)
Which is clearly not included in the range !!
Why isn't it $(3π/4)$?
I am very confused !
$\endgroup$ 32 Answers
$\begingroup$Conventions differ. Apparently your calculator is not using the same definition of arc-cotangent as you are.
$\endgroup$ 1 $\begingroup$The simple answer would be that your calculator has a different definition of arc-cotangent. It is not wrong to say that $-\pi / 4 $ is a solution of the equation $\cot (x) = -1$, and this is how your calculator understands it.
Nevertheless, there is a unique root of the equation $\cot (x) = -1$ lying in the (open) interval between $0$ and $\pi$. You will find it adding or substracting $\pi$ to any other solution an appopriate (integer) number of times (you can work out the actual number using the integer part function).
Hope this helps.
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