Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewNotice that graph does repeat itself 4 times in this range of x’s as it should.Let’s also note here that we can put all values of x into cosine (which won’t be thecase for most of the trig functions) and let’s also note that−1 ≤cos( x)≤ 1It is important to notice that cosine will never be larger than 1 or smaller than -1.This will be useful on occasion in a calculus class.2. y = cos( 2x)SolutionWe need to be a little careful with this graph. ( )not dealing with cos( x ) here. We are dealing with ( )cos x has a period of 2π , but we’recos 2x . In this case notice thatif we plug in x = π we will getcos( 2( π)) = cos( 2π) = cos( 0)= 1In this case the function starts to repeat itself after π instead of 2π ! So, this functionhas a period of π . So, we can expect the graph to repeat itself 8 times in the range−4π≤ x ≤ 4π. Here is that graph.Sure enough, there are twice as many cycles in this graph.In general we can get the period of cos( x)ω using the following.2πPeriod =ω© 2006 Paul Dawkins 54http://tutorial.math.lamar.edu/terms.aspx