Question

cos-1\(\left(-\frac{1}{\sqrt{2}}\right)\)

Answer 1

Let cos^-1\(\left(-\frac{1}{\sqrt{2}}\right)\) = y
∴ cos y = \(\left(-\frac{1}{\sqrt{2}}\right)\) = cos(\(\frac { π }{ 4 }\)) = cos(π – \(\frac { π }{ 4 }\))
The range of principal value branch of cos^-1 is [0, π].
∴ principal value of cos^-1\(\left(-\frac{1}{\sqrt{2}}\right)\) is \(\frac { 3π }{4 }\).