Question

Find the principal value of the following:

`cos^(-1) (-1/sqrt2)`

Answer 1

Let `cos^(-1)(-1/sqrt2)` = y

Then cos y = `- 1/sqrt2 = -cos (pi/4) = cos(pi - pi/4) = cos((3pi)/4)`

We know that the range of the principal value branch of cos⁻¹ is [0, π].

Where `(3pi)/4 ∈ [0, pi]`

`cos ((3pi)/4) = - 1/sqrt2`

Therefore, the principal value of `cos^(-1) (-1/sqrt2)` is `(3pi)/4`.