Transcript Trig or Treat MMC 20..

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
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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