# Math- Trigonometry

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The flowering of many commercially grown plants in greenhouses depends on the duration of natural darkness and daylight.  Short-day plants, such as chrysanthemums, need 12 or more hours of darkness before they will start to bloom.  Long day plants, such as carnations, need more than 12 hours of daylight.
The number of hours of daylight, h(t), varies with the latitude and the time of the year, t, where t is the day of the year.

1. Use the data in the table below to estimate when carnations will start to bloom in Ottawa, Regina, and Whitehorse.

Month Day of the Year Hours of Daylight on the Middle Day of Each Month - Ottawa Regina Whitehorse
January 15 8.9 8.5 6.6
February 45 10.1 10.1 9.2
March 75 11.6 11.8 11.7
April 106 13.3 13.7 14.5
May 136 14.7 17.1 22.2
June 167 15.4 16.4 18.8
July 197 15.1 15.6 17.5
August 228 13.8 14.6 15.8
September 259 12.2 12.7 13.8
October 289 10.7 10.8 10.2
November 320 9.3 9.1 7.6
December 350 8.6 8.1 5.9

2.Use sinusoidal regression (in radian measure) to create an algebraic model for Ottawa, Regina, and Whitehorse.  State the amplitude, period, and equation of the axis of the curve for each city.

3. Use the algebraic model for each city to calculate:
a) when the hours of daylight first exceed 12 hours.
b) the interval in the year when there are more than 12 hours of daylight.

4. Compare the blooming season for carnations in the three cities.

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