M1410406Part2

M1410406Part2 - (Section 4.6: Graphs of Other Trig...

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(Section 4.6: Graphs of Other Trig Functions) 4.63 Example Use the Frame Method to graph one cycle of the graph of y = 2tan 2 5 x 3 . (There are infinitely many possible cycles.) Solution Fortunately, b = 2 5 > 0 . If b < 0 , we would need to use the Even/Odd Properties. Remember that both tan and cot are odd functions. P ivot: p = 0, d = 3 ( ) C ycle shape: We have a tan graph with a = 2 > 0 , so we will use: A mplitude” = a = 2 = 2 P eriod = π b = 2/5 = 5 2 I ncrement = 1 4 Period ( ) = 1 4 5 2 = 5 8
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(Section 4.6: Graphs of Other Trig Functions) 4.64 The Frame Since there was no discernible phase shift, we see some nice symmetry between the positive and negative x -coordinates on this tan frame. Note: If you would prefer to start the labeling process at the “left-center” point, just as for sin and cos cycles, you could find the x -coordinate of a VA by setting the argument of tan equal to π 2 or 2 (for example), which correspond to asymptotes for y = tan x , and solving for x . Here: 2 5 x = 2 x = 5 2 2 x = 5 4 If you are dealing with a cot graph, then you would set the argument of cot equal to 0, just as for sin and cos graphs.
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(Section 4.6: Graphs of Other Trig Functions) 4.65 PART G: GRAPHS OF CSC AND SEC FUNCTIONS (“UP-U, DOWN-U” GRAPHS) Remember that csc x = 1 sin x . How can we use the graph of y = sin x to obtain the graph of y = csc x ? 1) Draw VAs through the x -intercepts (in purple) of the sin x graph. 2) Between any consecutive pair of VAs: If the sin x graph lies above the x -axis, then draw an “up-U” that has as its minimum point (in brown) the maximum point of the sin graph and that approaches both VAs. If the
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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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M1410406Part2 - (Section 4.6: Graphs of Other Trig...

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