http://www.ck12.org Chapter 5. Trigonometric Functions
Often the most challenging part of graphing periodic functions is labeling the axes. Since the period is 6π, start by
drawing the sinusoidal axis shifted appropriately. Then divide the 6πinto four parts so that the 5 guiding points of
the sine graph can be plotted with the amplitude and reflection in mind. The very last thing to do is to draw and
extend the curve. Many students try to draw the curve too early and end up having to redo their work.
Example C
A measuring stick on a dock measures high tide to be 18 feet and low tide to be 6 feet. It takes about 6 hours for the
tide to switch between low and high tides. Determine a graphical and algebraic model for the tides knowing that at
t=0 there is a high tide.
Solution: Usually the best course of action for word problems is to identify information, plot points, sketch and
then finally come up with an equation.
From the given information you can deduce the following points. Notice how the sinusoidal axis can be assumed to
be the average of the high and low tides.
TABLE5.6:
Time (hours) Water level (feet)
0 18
6 6
12 18
3 182 +^6 = 12
9 12By plotting those points and filling in the sinusoidal axis you can observe a cosine graph.