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

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

Grade:

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 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
askIITians faculty
Latika Leekha
askIITians Faculty 165 Points
6 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
askIITians Faculty

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