Question

Find the principal value of the following:

`cos^(-1) (-1/2)`

Answer 1

 Let `cos^(-1) (-1/2) = y`

Then, `cos y = -1/2`

= `-cos (pi/3)` 

= `cos (pi - pi/3)`

= `cos ((2pi)/3)`

We know that the range of the principal value branch of cos⁻¹ is [0, π] and `cos((2pi)/3) = -1/2`.

Therefore, the principal value of `cos^(-1) (-1/2)` is `(2pi)/3`.