Let s:R→[−1,1] be the sine function s(x)=sinx.
a. (i) Determine all intervals of the form (α,β) on which s is injective.
b. (ii) Show that no interval with length greater than π can serve as a domain on which s is injective.
c. (iii) Write any two distinct maximal intervals on which s is injective and state the corresponding inverse functions.