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 (b) Find a cosine curve that models the data 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 a cosine curve that models the data, we can use the formula y = A cos(B(x - C)) + D, where A, B, C, and D represent different factors. By performing the regression analysis on the given data, we can find the cosine curve that models the average daily sunspot count for the years 1975-2004.

Step-by-step explanation:

To find a cosine curve that models the data, we can use the formula:

y = A cos(B(x - C)) + D

where A represents the amplitude, B represents the period, C represents the phase shift, and D represents the vertical shift.

In this case, we are given a table of data with years and sunspot counts. We can use regression analysis to estimate the values of A, B, C, and D that best fit the data.

By performing the regression analysis on the given data, we can find the cosine curve that models the average daily sunspot count for the years 1975-2004.