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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).$$y=\sin (0.5 x+0.75)$$

## the lowest points are : $\mathrm{C}(7.9,-1), \mathrm{D}(20.5,-1)$

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### Video Transcript

the equation we have is why is equal to sign is your point. Find X plus 0.75 This equation can be rewritten as why is he called to side 0.5 times X plus 1.5. So for park caving in used equation and see that the amplitude is one. The period is 25 If I'd advise your 250.5 and that's equal to four pipe and then the phase shift these negative 1.5. So for part B, you can see the graph on the right side and for Park si. Also, we want to find the approximate coordinates. Often maximum point, which you can see on the draft are 1.642 in one and D coordinates off T may never point approximate coordinates of the minimum like a 7.9 to 5. And what now? For party? We want to find the exact quarters off these points. So we started a graph for why is equal to sign off 0.5 x so the craft would look like this. The pdf is four pipe. So the main point is two pi and the first of the maximum is at pie, and the minimum is at deep. I now for why is equal to sign. So your 0.5 times x plus 1.5. What we're gonna do is we're gonna take this maximum point and shifted 1.5 units to the left. Gonna take this maximum point and shifted 1.5 minutes to the left. So the exact coordinates would be for a maximum point. It would be pie minus 1.5 and one, and for the minimum point, the coordinates would be three by minus 1.5 and negative one.

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