Question

​Find the principal values of the following:
`cos^-1(-sqrt3/2)`

Answer 1

Let `cos^-1(-sqrt3/2) = y`

Then,

`cosy=-sqrt3/2`

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

Thus, 

`cosy=-sqrt3/2=cos((5pi)/6)`

`=>y=(5pi)/6in[0,pi]`

Hence, the principal value of `cos^-1(-sqrt3/2)` is `(5pi)/6.`