Applications of periodic functions.

1. The Bug on the Water Wheel
A water wheel with a 7.0 ft radius has 1.0 ft. submerged in the water as shown,
and rotates counterclockwise at 6.0 revolutions per minute. A bug is sitting on
the wheel at point B. You start your stopwatch, and two seconds later the bug at
point B is at its greatest height above the water. You are to model the distance 'h'
of the bug from the surface of the water in terms of the number of seconds 't' the
stopwatch reads.
(a) Sketch the graph.
(b) Write the algebraic equation of the sinusoid.
(c) How far is the bug above the water when t = 5.5 seconds?

3. 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.

4. 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?