Find the principal values of the following
(i) `sin^(-1) (sin 1)` (ii) `sin^(-1) (sin 2)`
(iii) `sin^(-1) (sin 10)`

Explanation

(i) Since `1 in [-pi//2, pi//2], sin^(-1) (sin 1) = 1`
(ii) Since `2 in [-pi//2, pi//2], sin^(-1) (sin 2) != 2`
`:. Sin^(-1) (sin 2) = sin^(-1) (sin (pi) -2))`
`= pi - 2 " as " (pi - 2) in [-pi//2, pi//2]`
(iii) `sin^(-1) (sin 10) = sin^(-1) (sin (3 pi - 10))`
`= 3 pi - 10 " as " (3 pi - 10) in [-pi//2, pi//2]`