Question

Why is `arcsin(sin(12pi))` = 0 and not 0 and `2pi`?

I thought it would be equal to 0 and `2pi`, but the answers said 0 only.

Answer 1

arcsine is a function so for each input there is only one output.

Explanation:

The range of arcsine is `-pi/2<=y<=pi/2`, each `x`-value in the domain is associated with only one `y`-value. The only value in the range of arcsine that is associated with `x=0`, which is the value of `sin(12pi)`, is `y=0`.