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The following scatter plot displays average monthly temperatures for Death Valley, California. (The averages were obtained using daily maximums.) Use the methods of Example 8 to find a periodic function of the form $y=A \sin (B t-C)+D$ whose values approximate the monthly temperatures. (No table is given; you will need to rely on the scatter plot and make estimates.)

(TABLE CANT COPY)

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so looking at the graph can gather that the maximum temperature happens in July, which is the seventh month, and that maximum temperatures approximately 815. And then the minimum temperature happens in January, which is the first month and that minimum temperatures approximately 65. So from here we can calculate the AMP acute A, which is maximum temperature minus the minimum temperature divided by two. So that would be 115 minus 65 divided by two. And that's equal to 25 since we're talking about Dempster change or a year, so the period is 12. From there we can Catholic be, which is to pine divided by the period. So to pine, divided by 12 gives I over six. Now, next thing we're gonna do is calculate the mean temperature and the mean temperature is the D vertical shift, which is maximum plus the minimum divided by two so backward people 215 plus 65 divided by two. And that's equal to 90. So now we can grow. And then when does the mean temperature first occur? So the mean temperature first up occurs, and April and April is the fourth month. So that would be teams equal to four. So we can write the equation. Now. Why is equal to 25 sign off high over six times T minus four plus 90 Or we have why is equal to 25 Sign off high over six T minus two pi over fee plus 19.