Calculus: Early Transcendentals, Chapter 1, 1.6, Section 1.6, Problem 12

Determine whether $g(x) = \cos x$ is one-to-one.
Remember that the graph of $g(x) = \cos x$ is repeating over intervals. So if we use horizontal
line test, the line will intersect the graph at many points. Thus, $g(x) = \cos x$ is not one-to-one.