Find the principal value of the following
(i) `cos^(-1) (cos 3)` (ii) `cos^(-1) (cos 4)`
(iii) `cos^(-1) (cos 15)` (iv) `cos^(-1) (cos 30)`
(v) `cos^(-1) (cos 50)` (vi) `cos^(-1) (cos.(48pi)/(7))`

Explanation

(i) Since `3 in [0, pi], cos^(-1) (cos 3) = 3`
(ii) Since `4 !in [0, pi], cos^(-1) (cos 4) != 4`
`:. Cos^(-1) (cos 4) = 2pi - 4`
(iii) `cos^(-1) (cos 15) = 15 - 4 pi`
(iv) `cos^(-1) (cos 30) = 10 pi - 30`
(v) `cos^(-1) (cos 50) = 16 pi - 50`
(vi) `cos^(-1) (cos.(48pi)/(7)) = cos^(-1) (cos(6pi + (6pi)/(7)))`
`= cos^(-1) (cos.(6pi)/(7)) = (6pi)/(7)`