# Find the principal value of tan-1 (-1).

SHAIK AASIF AHAMED
8 years ago
Hello student,
Let tan-1(-1)=x
so tan x = -1
tan x =tan ($\tiny -\pi /4$)
As we know that the range of tan-1is ($\tiny -\pi /2,\pi /2$)
so x=$\tiny -\pi /4$
So the principal value oftan-1(-1)=$\tiny -\pi /4$
Thanks and Regards
Shaik Aasif
Latika Leekha
8 years ago
Let us assume tan-1(-1) = y.
Then we have tan y = -1
This can be written as tan y = tan (-$\Pi$/4)
Also, we know that the range of principal value branch of tan-1y is (-$\Pi$/2, $\Pi$/2),
hence, this means that y = -$\Pi$/4.
Hence, the principal value of tan-1(-1) is -$\Pi$/4.
Thanks & Regards
Latika Leekha