Graphing the Trigonometric Functions•Section 5.1105xy0−8−6−4−22468π4π23π4π5π43π27π42π−π4−π2−3π4−π−5π4−3π2−7π4−2πy=tanxFigure 5.1.6Graph ofy=tanxRecall that the tangent is positive for angles in QI and QIII, and is negative in QII andQIV, and that is indeed what the graph in Figure 5.1.6 shows. We know that tanxis notdefined when cosx=0, i.e. at odd multiples ofπ2:x=±π2,±3π2,±5π2, etc. We can figure outwhat happensnearthose angles by looking at the sine and cosine functions. For example,forxin QI nearπ2, sinxand cosxare both positive, with sinxvery close to 1 and cosxveryclose to 0, so the quotient tanx=sinxcosxis a positive number that is very large. And the closerxgets toπ2, the larger tanxgets. Thus,x=π2is avertical asymptoteof the graph ofy=tanx.Likewise, forxin QII very close toπ2, sinxis very close to 1 and cosxis negative and veryclose to 0, so the quotient tanx=sinxcosxis a negative number that is very large, and it gets
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