Question

cos^-1(-\(\frac { 1 }{ 2 }\))

Answer 1

Let cos^-1(-\(\frac { 1 }{ 2 }\)) = y
∴ cos y = –\(\frac { 1 }{ 2 }\) = – cos\(\frac { π }{ 3 }\) = cos(π – \(\frac { π }{ 3 }\)
= cos \(\frac { 2π }{ 3 }\)
The range of principal value branch is (0, π)
∴ principal value of cos^-1(-\(\frac { 1 }{ 2 }\)) is \(\frac { 2π }{ 3 }\).