Applications of periodic functions; a beginning. Moving between equations, graphs and tables of values.

1. How many periods are illustrated in each graph?
How many revolutions (in radians and degrees) are illustrated in each graph?
Periods =
Radians Rotated =
Degrees Rotated =
Periods =
Radians Rotated =
Degrees Rotated =
Periods =
Radians Rotated =
Degrees Rotated =

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

3. Determine approximate values for the parameters 'a', 'b', 'c', and 'd' from the
graphs, and then write the equations of each graph as a sinusoidal function in
the form: y = a sin b(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.
x -1 -0.5 0 0.5 1 1.5 2 2.5
y1 -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.