More Applications of Periodic Functions.

1. Trigonometric
Modeling
Waterwheel by
flickr user lndhslf72

2. State the amplitude, period, horizontal shift, and vertical shift for each of the
following: HOMEWORK
amplitude: amplitude:
period: period:
horizontal shift: horizontal shift:
vertical shift: vertical shift:

3. State the amplitude, period, horizontal shift, and vertical shift for each of the
following: HOMEWORK
amplitude: amplitude:
period: period:
horizontal shift: horizontal shift:
vertical shift: vertical shift:
ƒ(x) = AsinB(x - C) + D

4. Enter the values into your calculator, and use a sinusoidal regression to
determine the equation. Round the values of the parameters to one decimal
place. HOMEWORK
x -1 -0.5 0 0.5 1 1.5 2 2.5
y 1 -2.6 -5.6 -5.4 -2 1.4 1.6 -1.4

5. Jud was working with sinusoidal data, but lost all of it except for two
points. A maximum point was (3, 13) and a minimum point next to it
was (7, 1). Write a sinusoidal equation that matches Jud's data.
ƒ(x) = AsinB(x - C) + D

6. 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?

7. 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.
(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?