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

1 Answer
Jul 20, 2015

tan^-1(-1) = -pi/4

Explanation:

sin(pi/4) = sqrt(2)/2 so sin(-pi/4) = -sqrt(2)/2

cos(pi/4) = sqrt(2)/2 so cos(-pi/4) = sqrt(2)/2

tan(-pi/4) = sin(-pi/4)/cos(-pi/4) = (-sqrt(2)/2)/(sqrt(2)/2) = -1

Note that tan(theta) is periodic with period pi. So we find:

tan(kpi-pi/4) = -1 for any integer k.

However, the principal value denoted tan^(-1) is chosen to lie in the range (-pi/2, pi/2), which includes -pi/4. So that is the value of tan^(-1)(-1)