Question

Find a possible formula for the trigonometric function whose values are in the following table (note the values in the table may be slightly rounded):

x 0.00 0.17 0.33 0.50 0.67 0.83 1.00 1.17 1.33 1.50 1.67 1.83 2.00
g(x) 4.00 5.50 6.60 7.00 6.60 5.50 4.00 2.50 1.40 1.00 1.40 2.50 4.00

Answer 1

SKETCH A GRAPH !!
add all g values and divide by 13 to get mean
high = 7-mean
low = mean -1
amplitude A = (hing - low)/2

y = A sin (w t + phi)

w t = 2 pi in one period from 7 to 1 and back up so w T = pi from 7 to 1

Answer 2

SKETCH A GRAPH !!
add all g values and divide by 13 to get mean
high = 7-mean
low = mean -1
amplitude A = (hing - low)/2

y = A sin (w t + phi)

w T = 2 pi in one period from 7 to 1 and back up so use twice the time from 7 down to 1 for T and w = 2 pi/T