Applications of Sinusoidal Functions

Applications of Sinusoidal Functions – PRACTICE 1. Sunsets are later in the summer than in the winter. For planning a sunset dinner cruise through the 30,000 Islands, the cruise planners may find the time, t in hours (on a 24-hour clock) of the sunset on the n th day of the year using the equation:   43 . 18 37 . 79 986 . 0 sin 75 . 1    n t a) What are reasonable values for t in this situation? b) What are reasonable values for n in this situation? c) Determine the time of the sunset on Nadia’s birthday of July 26 (the 207 th day of the year). d) Determine the day(s) of the year when the sunset time is at 6:00 pm (18:00 hours). 2. All towers and skyscrapers are designed to sway with the wind. When standing on the glass floor of the CN Tower, the equation of the horizontal sway is   x y 023 . 30 sin 40  , where y , is the horizontal sway in centimetres and x , is the time in seconds. (Round answers to the nearest whole number.) a) Graph the equation. b) State the maximum value of sway and the time at which it occurs. c) State the minimum value of sway and the time at which it occurs. d) State the mean value of sway and the time at which it occurs. e) If a guest arrives on the glass floor at time = 0, how far will the guest have swayed from the horizontal after 2.034 seconds? f) If a guest arrives on the glass floor at time = 0, how many seconds will have elapsed before the guest has swayed 20 cm from the horizontal? 3. The average monthly temperature in a region of Australia is modeled by the function     9 270 30 sin 23     m m T , where T is the temperature in degrees Celsius and m is the month of the year. For m = 0, the month is January. a) Graph   m T for 1 year. (Hint: Use m = 0, 3, 6, etc.) b) State the range of the function. c) In which month does the region reach its maximum temperature? Minimum? d) If travelers wish to tour Australia when the temperature is below 20 o C, which months should be chosen for their tour? Answers: 1. a), b) answers may vary c) 7:53 pm d) 66 th day or 299 th day 2. b) max value 40 at 3 sec c) min value – 40 at 9 sec d) mean value 0 at 6, 12 sec e) 35 min f) 1 sec 3. b) 32 14    T c) max – January, min – June d) m = 10