Example 2: Arc Sine

Find arcsin(-1).

From Table 7.1.1,

sin(3π/2) = -1.

But 3π/2 is not in the interval [-π/2, π/2]. Using sin (θ + 2nπ) = sin θ, we have

sin (-π/2) = sin (3π/2) = -1,

so 

arcsin (-1) = - π/2.