Question

Find the principal value of the following: `sin^-1 (1/2)`

Answer 1

The principal value branch of `sin^-1 x  "is" [- pi/2, pi/2]`.

Let `sin^-1 (1/2) = α, "where" (-pi)/(2) ≤ α ≤ pi/(2)`

∴ `sin α = 1/2 = sin  pi/(6)`

∴ α = `pi/(6)           ...[ ∵ - pi/2 ≤ pi/6 ≤ pi/2 ]`

∴ the principal value of `sin^-1 (1/2) "is" pi/(6)`.