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

Question

tan^-1(-1)

Answer 1

Let tan^-1(-1) = y.
∴ tan y = – 1 = tan\(\frac { π }{ 4 }\)) = tan(\(\frac { -π }{ 4 }\))
The range of principal value branch of tan^-1 is [-\(\frac { π }{ 2 }\), \(\frac { π }{ 2 }\)]
∴ principal value of tan^-1(-1) is \(\frac { π }{4 }\).