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Topic: Triginometry and Circular Functions
Replies: 0

 Richard Sisley Posts: 4,189 Registered: 12/6/04
Triginometry and Circular Functions
Posted: Mar 31, 1997 8:14 AM

Regarding presenting trigonometry to students so that they see some
reason for it:

In a sequence of courses we have developed as the W. M. Keck Curriculum
Project the students first see sine and cosine in the context of writing
2X2 matrices for origin centered rotations. They then immediately see
triangles created using connected scatter plots rotated when rotation
matrices are used to guide the computation of the coordinates of the
images of the vertices.

The complex number system is developed using simple transformations,
including origin centered rotations. The motivation to do this is to
try to make sense of square roots of negative real numbers which arise
sometimes when using the quadratic formula.

Later, data is collected as a slinky toy is put in motion over a motion
sensor. With a little care the frequence an amplitudes of the
oscillations can be made rather constant. Here sine wave functions
provide good models for the data.

We have found that navagation problems provide a good motivation for
applying sine and cosine to triangles. Given the heading and distance
for the first two legs of a journey, how far is one from the starting
point?

We also apply triangle trigonometry to computing the distance between
two points on a spherical model of the Earth given their longitude and
latitude. This is done without bringing in the Spherical Law of Cosines
with no explanation.

Paramatric simulations of projectile motion also naturally involved sine
and cosine to describe separately the horizontal and vertical components
of the motion.

Dick Sisley