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Pre-Calc Exam Notes 105

# Pre-Calc Exam Notes 105 - Graphing the Trigonometric...

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Graphing the Trigonometric Functions Section 5.1 105 x y 0 8 6 4 2 2 4 6 8 π 4 π 2 3 π 4 π 5 π 4 3 π 2 7 π 4 2 π π 4 π 2 3 π 4 π 5 π 4 3 π 2 7 π 4 2 π y = tan x Figure 5.1.6 Graph of y = tan x Recall that the tangent is positive for angles in QI and QIII, and is negative in QII and QIV, and that is indeed what the graph in Figure 5.1.6 shows. We know that tan x is not defined when cos x = 0, i.e. at odd multiples of π 2 : x π 2 , ± 3 π 2 , ± 5 π 2 , etc. We can figure out what happens near those angles by looking at the sine and cosine functions. For example, for x in QI near π 2 , sin x and cos x are both positive, with sin x very close to 1 and cos x very close to 0, so the quotient tan x = sin x cos x is a positive number that is very large. And the closer x gets to π 2 , the larger tan x gets. Thus, x = π 2 is a vertical asymptote of the graph of y = tan x . Likewise, for x in QII very close to π 2 , sin x is very close to 1 and cos x is negative and very close to 0, so the quotient tan x = sin x cos x is a negative number that is very large, and it gets
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