Sketch one cycle of the cosine function y= cos 2θ

Based on function transformations, the graph of y= cos(2θ), is the same as the graph of y= cos(θ), with a component B of 2, in which case, it means the period is the only thing that differs

well the period for this function will then be  

so, the graph of is, the same as y= cos(θ), just shrunk by half horizontally