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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).$$y=0.02 \cos (0.01 \pi x-4 \pi)$$

## the lowest points are : $\mathrm{D}(500,-2.5), \mathrm{E}(700,-2.5)$

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### Video Transcript

So we have the equation. Why is equal to 0.2 co sign of zero points your one high X minus foreplay. This equation can be rewritten as why is equal to zero point you to co sign cause you know, point is, you know, one high times X minus 400. So from this equation, we can see that the app acute is as your points you're too. The period is two pi divided buys, you know, points your one pie and that's equal to 200. And then the phase shift his 400 for part me, you can see the graph is drawn on the right side. So from the graph, you can see that the ambiguities, your points, you're too. You can see that the period is 400 then for part c, you can actually see it at the corden softy. Maximum point are zero and you opened your to and another maximum occurs at 200 your points you are too. And the quarter mitts off. The minimum point are 100 and negative zero points group to now for part D. We can see that the phase shift, which is a 400 that is a multiple off the period. So since the period is 200 we can see that the face shift is actually two times the period. Therefore, what that means is that maximum and minimum points can simply read from the graph and those would be the exact coordinates.

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