```THE SINE FUNCTION

Ronald G. Sienkiewicz          Prosser Vocational High School
Chicago, IL 60639
1-312-637-5556

Objectives:
To familiarize the students with the concept of the sine function by
defining, by graphing, by computer generating, by using a "shop created"
blackboard sine wave generator, and by presenting examples of natural phenomena
which result in sine wave motion.

Materials:
1) a plexiglass sine wave generator; 2) blackboard and chalk; 3) a computer
and CRT with appropriate software; 4) a handout containing computer generated sine
graphs, a table of values of the sine function from 0 to 90, a pictorial
definition of the sine function, a copy from a Physics textbook of a section
explaining periodic  and oscillating motion.

Strategies:
In teaching this concept, I began by talking about an elementary example of a
wave i.e. an ocean wave with its attendant amplitude and periodicity. I then
changed models and demonstrated a sine wave on the chalkboard by using a shop-
created sine wave generator. Here, I was able to be somewhat more mathematical by
relating the height of any angle to movement on the Y-axis and lateral distance as
movement on the X-axis. This lead to a formal mathematical definition of the sine
function. Next, I graphed the function Y=sin X. I did this by using values of 90,
180, 270, & 360 degrees (quadrantal angles). Using these values, I showed that the
value of the function oscillates between 1, 0, & -1. In the same context, I showed
how any intermediate angle, plugged into the equation, will likewise be a point of
the same graph. The values for the intermediate angles were obtained from the
table of values provided in the handout.
Following this, I went to the computer. Writing an equation on the chalkboard
and asking the students to predict its graph, I was able to quickly and
efficiently run through several variations of the sine function without the
tediousness of using the chalkboard. Incidentally, although it might be considered
of marginal relevance, we did review the programming that created these graphs.
Next, I discussed the phenomena of the sine wave in nature. The handout contained
a copy of a section of a Physics text book dealing with oscillations and periodic
movement. The significant idea here, being that this type of motion (the movement
of a pendulum and the motion of a mass at the end of a spring-natural phenomena)
will always be mathematically expressed in terms of sines and cosines.
Thus, my presentation was concluded. I intended to make an interdisciplinary
presentation on sine waves. In this way, I hope that I have given the students a
multidimensional and hopefully memorable view of the nature and meaning of the
sine wave.

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