Find the principal value of each of the following: cos^-1(-1/√2)

Question

Find the principal value of each of the following:

\(cos^{-1}(-\frac 1{\sqrt2})\)

Answer 1

Let \(cos^{-1}(-\frac 1{\sqrt2})\) = y

Then,

We know that the range of the principal value branch of cos^-1 is [0, π ] and cos \((\frac{3\pi}4)\) = \(-\frac{1}{\sqrt2}\).

Therefore, the principal value of cos^-1\((-\frac{1}{\sqrt2})\) is \(\frac{3\pi}4.\)