To determine To sketch: At least two cycles of graph of the function y = 0.5 cot 2 x , if 0.5 is changed to 5. Explanation Consider the function y = 0.5 cot 2 x . If 0.5 is changed to 5 in the above function, then the function becomes y = 5 cot 2 x . Since the period for cot x is π , the period of cot 2 x will be π 2 . Thus, one-fourth of the period will be, 1 4 ( π 2 ) = π 8 . Notice that the displacement is zero. That is, the curve starts at 0 and starts repeating π 2 units to the right of 0. Since the period is π 2 , the one complete cycle ends at 0 + π 2 = π 2 . Thus, the two complete cycles ends at 0 + 2 ( π 2 ) = π . That is, two cycles occur between x = 0 and x = π . The important values for the first cycle are at 0 , 0 + π 8 , 0 + 2 ( π 8 ) , 0 + 3 ( π 8 ) and 0 + 4 ( π 8 ) . That is, at 0 , π 8 , π 4 , 3 π 8 and π 2 . Substitute x = 0 in the equation y = 5 cot 2 x . y = 5 cot 2 x = 5 cot ( 2 × 0 ) = 5 cot ( 0 ) = Undefined That is, x = 0 is an asymptote of the curve y = 5 cot 2 x . Similarly, obtain the values of the function at π 8 , π 4 , 3 π 8 and π 2

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Chapter 10.4, Problem 1E

To determine

To sketch: At least two cycles of graph of the function y=0.5cot2x, if 0.5 is changed to 5.

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Chapter 10.3, Problem 44E

Chapter 10.4, Problem 2E

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Basic Technical Mathematics

Ch. 10.1 - For the graph of y = −6 sin x, set up a table of...Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - In Exercises 3–6, complete the following table for...Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - In Exercises 7–22, give the amplitude and sketch...Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E

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