More applications of periodic functions and review for test.

1. Average Monthly Temperature in Winnipeg
The chart below shows Winnipeg's average monthly temperature.
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month # 1 2 3 4 5 6 7 8 9 10 11 12
Temp ºC -16 -13 -6 4 12 16 20 18 12 5 -5 -13
(a) Sketch a graph and write the equation of the related sinusoid.

2. Average Monthly Temperature in Winnipeg
The chart below shows Winnipeg's average monthly temperature.
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month # 1 2 3 4 5 6 7 8 9 10 11 12
Temp ºC -16 -13 -6 4 12 16 20 18 12 5 -5 -13
(b) Find the regression equation of this relation using your graphing calculator.
(c) Does the relation between temperature and time appear to be sinusoidal?
Explain.
(d) What is the average temperature for the year?

3. Apogee and Perigee
A spacecraft is in an elliptical orbit around the
earth as shown in the diagram. At its perigee the
spacecraft is at its lowest point above the earth's
surface, and at its apogee it is at its highest point
above the earth.
The equation: describes the spacecraft's
distance from the earth over time, where 'x' represents the time in
minutes, and 'y' the distance in kilometres. Write answers for the
following questions, and then click on Answer to check your work.
(a) How long does it take for the spacecraft to fly around the earth?
(b) What are the distances at apogee and perigee?

4. The Water Heater and the Hot Tub
An electric heater cuts in and out on a cyclical basis as it heats the water in a
hot tub. The water temperature 'C' in degrees Celsius varies sinusoidally with
time 't'. The thermostat is set to turn the heater on when the temperature drops
to 36°C and off when it reaches 42°C. In order to measure the period, a timer
was started at 0 when the heater cut in. The heater turned off 30 minutes later
and turned on again after another 30 minutes.
(a) Sketch the graph of the function for 0 ≤ t ≤ 60.
(b) Write the equation expressing temperature, C, in terms of time, t.
(c) Use your equation to determine the temperature 10 minutes after the
heater turns on.