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python# Finding the amplitude 'a'
max_sunrise = df_beijing_melted['Sunrise Time'].max()
min_sunrise = df_beijing_melted['Sunrise Time'].min()
amplitude_a = (max_sunrise - min_sunrise) / 2
# Finding the vertical shift 'd'
vertical_shift_d = (max_sunrise + min_sunrise) / 2
# Estimating the horizontal shift 'c'
# We'll assume the horizontal shift is at the month corresponding to the latest sunrise (maximum value)
month_of_latest_sunrise = df_beijing_melted[df_beijing_melted['Sunrise Time'] == max_sunrise]['Month'].values[0]
# Estimating the horizontal shift 'c'
# We need to adjust for the fact that the max sunrise time might not exactly be at 0 amplitude due to the shift.
# We'll take an approximate value by taking the month and adjusting for the day
day_of_latest_sunrise = df_beijing_melted[df_beijing_melted['Sunrise Time'] == max_sunrise]['Day'].values[0]
horizontal_shift_c = month_of_latest_sunrise + (day_of_latest_sunrise - 1) / 30
# The value of 'b' can be calculated knowing the period of the sine function is one year (12 months).
# Therefore, b = 2π / period
period = 12 # in months
b_value =
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