The latest sunrise in Montreal was on Dec. 22 at 9:15 AM . According to the almanac, the earliest sunrise occurred on the 22nd of June at 3:15 AM . The sunrise times on other dates can be predicted using a sinusoidal equation.
**Assume there is no daylight savings time in Montreal.**
Read the given info and convert it into information that can be used in an equation. For example, the time is not going to be written 9:15 on the graph but 9.25 because 15 min. is a quarter of an hour.
Make two lists for the parameters A, B, C & D. One set will be used for the cosine equation and the other will be used for the sine equation.
Find the parameters in the mean of DABC [stretches before translations]. To find parameter D, add the min. and max. value and then divide by 2 to find the sinusoidal axis .
To find parameter A, subtract the average value from the maximum value to get A.
Parameter B is equal to 2 π divided by the period, which happens to be the number of days in a year; 364.
The phase shift (C) is found depending on what kind of equation is being used. If the cosine equation is being found, the maximum value is usually on the y-axis. But the information tells us that the maximum value occurs on Dec. 22, 9 days before Jan. 1 [the y-axis].
The phase shift in the sine equation is determined by finding out the distance of the average value to the y-axis.
Finally, to get the equations, plug in the values found into the general formula.
Find out what the day of the year September 7 th is by adding up the total number of days in each month up to the given date, assuming there is no daylight savings time.
Since d lies along the x-axis, treat the number of days as an x-coordinate and plug in as d in the formula, either sine or cosine and solve.
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