This worksheet explores the injectivity and surjectivity of the function [math]f(x)=\sin(x)[/math]. As a function [math]f:\mathbb{R}\to\mathbb{R}[/math], it is neither injective nor surjective. But by carefully restricting the domain and codomain, we can define a new function that is either injective, or surjective, or both.

[list=1] [*] Adjust [color=#0000ff][math]a[/math][/color] and [color=#0000ff][math]b[/math][/color] to restrict the domain of [math]f[/math] to an interval on which it is injective. [*] Adjust [color=#ff0000][math]c[/math][/color] and [color=#ff0000][math]d[/math][/color] to restrict the codomain of [math]f[/math] to an interval on which it is surjective. [/list]