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

Algebra/Trig ReviewIf ω > 1we can expect a period smaller than 2π and so the graph will oscillate faster.Likewise, if ω < 1 we can expect a period larger than 2π and so the graph willoscillate slower.Note that the period does not affect how large cosine will get. We still have−1 ≤cos 2x≤ 13. y = 5cos( 2x)( )SolutionIn this case I added a 5 in front of the cosine. All that this will do is increase how bigcosine will get. The number in front of the cosine or sine is called the amplitude.Here’s the graph of this function.Note the scale on the y-axis for this problem and do not confuse it with the previousgraph. The y-axis scales are different!In general,−R≤ Rcos( ω x)≤ R4. y = sin ( x)SolutionAs with the first problem in this section there really isn’t a lot to do other than graphit. Here is the graph on the range −4π≤ x ≤ 4π.© 2006 Paul Dawkins 55http://tutorial.math.lamar.edu/terms.aspx