When defining the inverse cosine function: cos^-1(x), the domain of the cos(theta) had to be restricted to angles theta on the interval:[0 pie,] only. Why?

Question

When defining the inverse cosine function: cos^-1(x), the domain of the cos(theta) had to be restricted to angles theta on the interval:[0 pie,] only. Why?

Answer 1

Because on interval [0, π] function f(x) = cosx take all values from 1 = cos0 to -1 = cosπ and on this

interval each value cosx takes only once, so it one-to-one function