Question:
Formula for a sine curve given the amplitude and either the period, frequency or angular frequency.
(i) In london in 2002, the maximum number of daylight hours in a day was 16.63, and this was recorded in week 25.The minimum number of daylight hours in a day was 7.82, and this was recorded in week 51. The number of daylight hours in a day can be modelled approximately by using a sine function.
Use the information given above to find the following values, showing details of your calculations.
(a) the amplitude of the function,
(b) the period (in weeks) of the function,
(c) the vertical displacement of the curve
(d) the phase shifdt of the curve
(ii) (a) Using your answers to part (i), write down the equation of the curve, defining your variables clearly.
(b) Use this model to determine approximately, how much daylight there was per day in London in week 13 of 2002