Trig or Treat MMC 2013 Lisa Parker Michael Keyton

What Trigonometry should students know and What Trigonometry should be taught?

Trigonometric Topics Notation: sides a, b, c; angles A, B, C; At the most elementary – Right Triangle Trigonometry

They should know:

Definitions of the trig functions and their inverses from both similar triangles and circles Solve triangles: Law of Sines, Cosines

Values: Degrees and Radians 30, 45, 60, 90 and rotations Identities: Reduction Sum and Difference Double angle Half-angle

In general, students learn mathematics for a variety of reasons. The topics chosen should emphasize all these reasons. Some properties are needed for future study, appreciation of the history of mathematics, comprehension of the uses in real world applications, logical sequencing of thoughts, and problem solving.

TREAT TIME Compute values for the 36 degree angle. Using it we can then compute the values for all angles that are multiples of 3 degrees.

IDENTITIES

Many other identities have been developed to aid with computation limitations. But now that we have and can use calculators and computers, many of these have been virtually rendered archaic.

However, one that I like that is rarely seen, but potentially useful: a = b sin(C) + c sin(B) which follows from the Law of Sines and the Angle Sum Formula gtW

From this identity, the Law of Cosines follows easily.

The proof is left for you as an exercise.

Now for a Mixed Bag of Goodies W

Time for The Circumcenter, The Incenter, The Excenters, and The Orthocenter.

THANKS Lisa and Michael