Question

​Find the principal values of the following:

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

Answer 1

Let `cos^-1(-1/sqrt2) = y`

Then, 

`cosy=-1/sqrt2`

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

Thus,

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

`=>y=(3pi)/4 in[0,pi]`

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