M1410406Part1

M1410406Part1 - (Section 4.6 Graphs of Other Trig Functions...

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Unformatted text preview: (Section 4.6: Graphs of Other Trig Functions) 4.53 SECTION 4.6: GRAPHS OF OTHER TRIG FUNCTIONS PART A: GRAPH f θ ( ) = tan θ We begin by tracing the slope of the terminal side of the standard angle θ as θ increases from 0 towards π 2 and as it decreases from 0 towards − π 2 . The information on slopes is in purple in the figure below. We obtain one cycle of the graph of f θ ( ) = tan θ . The period is π , not 2 π . Why? (Section 4.6: Graphs of Other Trig Functions) 4.54 Observe that the behavior of f on the interval π 2 , 3 π 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ is identical to its behavior on the interval − π 2 , π 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ : (Section 4.6: Graphs of Other Trig Functions) 4.55 One cycle: Three cycles (not framed): You can see that f θ ( ) = tan θ is odd due to the symmetry about the origin. Observe that the vertical asymptotes (VAs) naturally divide the graph into cycles. “Framing” One Cycle The setup for the frame of a tan or cot function has a number of differences from our setup in the last section : • (Warning!) When we graph a tan function, the central point, not the “left-center” point, of the frame will be our pivot; it is typically a point on the graph. (When we graph a cot function, the “left-center” point will again be our pivot; it is typically not a point on the graph.) For now, the pivot is the point 0,0 ( ) . • The left and right edges of the frame correspond to vertical asymptotes (VAs). Warning: When you are told to graph a trig function, you are expected to draw in the vertical asymptotes (if any) as dashed lines....
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This note was uploaded on 09/08/2011 for the course MATH 141 taught by Professor Staff during the Fall '11 term at Mesa CC.

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M1410406Part1 - (Section 4.6 Graphs of Other Trig Functions...

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