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# (a) Using pencil and paper, not a graphing utility, determine the amplitude, period, and (where appropriate) phase shift for each function.(b) Use a graphing utility to graph each function for two complete cycles. [In choosing an appropriate viewing rectangle, you will need to use the information obtained in part (a).](c) Use the graphing utility to estimate the coordinates of the highest and the lowest points on the graph.(d) Use the information obtained in part (a) to specify the exact values for the coordinates that you estimated in part (c).$$y=0.02 \cos (100 \pi x-4 \pi)$$

## the lowest points are : $\mathrm{D}(0.05,-2.5), \mathrm{E}(0.07,-2.5)$

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

so we have the equation. Why is equal to 0.2 course? Sign off 100 high X minus four pine. So this can be rewritten as why is he quit? Choose your points. Your to co sign off 100 pie times X minus 0.4 So from that equation, parking we consult the after cute is euro points. You're too on the period is two pi divided by ah 100 pipe, which is 1/50 or because real 1000.2 and then the fish shift. His zero points you four and you can see the graph on the right side. And for part C, get the organs off the maximum and minimum points, so there's a maximum at X is equal to zero. Y is equal to zero point. You're too. There's another maximum at your excessive 4 to 0.2 And why? Because your question or two and there's one minimum and X equal to 0.1 and negatives your points. You're too, so you can get the answers to heart. See, also from the graph now for party. What we're seeing is that the face shift is a multiple off period, so phase shift is actually two times a period, and what that means is that the maximum and minimum corners can be read from the draft.

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University