Question

Find the principal value of the following:

`cos^(-1) (sqrt3/2)`

Answer 1

Let `cos^(-1) (sqrt3/2) = y`

Then, `cos y = sqrt3/2 = cos (pi/6)`

We know that the range of the principal value branch of cos⁻¹ is

[0, π] and `cos (pi/6) = sqrt3/2`

Therefore, the principal value of `cos^(-1) (sqrt3/2)` is `pi/6`.