Question

Sunspots are relatively ""cool"" regions on the sun that appear as dark spots when observed through special solar filters. The number of sunspots varies in an 11 -year cycle. The table gives the average daily sunspot count for the years 1975-2004 (d) Use a graphing calculator to find the sine curve that best fits the data (as in Example 2). Compare to your answer in part (b). year sunspots year sunspots 1975 16 1990 143 1976 13 1991 146 1977 28 1992 94 1978 93 1993 55 1979 155 1994 30 1980 155 1995 18 1981 140 1996 9 1982 116 1997 21 1983 67 1998 64 1984 46 1999 93 1985 18 2000 119 1986 13 2001 111 1987 29 2002 104 1988 100 2003 64 1989 158 2004 40

Answer 1

To find the sine curve that best fits the data, you can use a graphing calculator. Follow these steps: enter the data, plot the points, go to the STAT menu, select SinReg, input the lists, and the calculator will display the best fitting sine curve. Using a graphing calculator provides a more accurate representation of the data.

Step-by-step explanation:

To find the sine curve that best fits the data, we can use a graphing calculator. Here are the steps:

1. Enter the given data into the lists on the graphing calculator. Let the year (d) values be the x-values and the sunspot count values be the y-values.
2. Plot the points on the graphing calculator.
3. Go to the STAT menu and select CALC option.
4. Select option 5 for SinReg (sine regression).
5. Input L1 and L2 as the lists (assuming the years are in L1 and sunspot counts are in L2).
6. Press enter and the graphing calculator will display the sine curve that best fits the data.

In comparison to part (b), where you hand-drew the best fitting sine curve, using a graphing calculator provides a more accurate representation of the data and the sine curve.