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

Algebra/Trig ReviewIn the case of tangent we have to be careful when plugging x’s in since tangentsin xdoesn’t exist wherever cosine is zero (remember that tan x = ). Tangent will notcos xexist at5π 3π π π 3π 5πx = , − , − , − , , , , 2 2 2 2 2 2and the graph will have asymptotes at these points. Here is the graph of tangent on5π5πthe range − < x < .2 2Finally, a couple of quick properties about Rtan( x)−∞ < Rtan ( ω x)< ∞For the period remember that ( )ω .πPeriod =ωtan x has a period of π unlike sine and cosine andthat accounts for the absence of the 2 in the numerator that was there for sine andcosine.7. y = sec( x)SolutionAs with tangent we will have to avoid x’s for which cosine is zero (remember that1sec x = cos x). Secant will not exist at5π 3π π π 3π 5πx = , − , − , − , , , , 2 2 2 2 2 2and the graph will have asymptotes at these points. Here is the graph of secant on the5π5πrange − < x < .2 2© 2006 Paul Dawkins 57http://tutorial.math.lamar.edu/terms.aspx