Question

Find the principal value of the following:

tan^-1 (-1)

Answer 1

tan^-1 (-1) = y

(-1) = tan y where `(-pi)/2 <= y <= pi/2`

(or) tan y = – 1

tan y = tan`(- pi/4) (because tan  pi/4 = 1)`

∴ y = `- pi/4  [because tan(- pi/4) = - tan(pi/4) = - 1]` 

∴ The principal value of tan^-1 (-1) is `- pi/4`.