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Q&A #403

Teachers' Lounge Discussion: Number Theory and Trigonometry

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From: RON <rselby@cinci.rr.com>
To: Teacher2Teacher Public Discussion
Date: 2003061022:07:12
Subject: Re: theory in trigonometry

tri-gon-ometry: (metry) the measurement of (tri) three sided (gon) two
dimensional figures.

The issue here is basically to understand the relationships between
the sides and angles in a triangle.

Angles can be measured in a variety of systems. Degrees, minutes, and
seconds (DMS) is usually used in beginning courses. Radian measure is
usually used in higher level courses. (2 pi radians = 360 degrees.)
Other systems such as gradients are more suited to specific
occupations.

Sides are usually measured in length units, sometimes simply expressed
as a unitless number in a math class.

Suggested reading topics include:

1) the pythagorean theorem

2) the law of sines

3) the law of cosines

4) the law of tangents

5) vector anaysis

6) trigonometric functions, such as sine, cosine, tangent, secant,
cosecant, cotangent, and their inverses. ( Most scientific calculators
will have buttons for some of these.)

Regarding the last topic (#6), some texts will take the unit circle
approach, others will base the definitions upon side positions in a
right triangle.

Any pre-calculus text will have an extensive section devoted to these
topics. The prerequisite for this material would be a good foundation
in algebra.

Advanced topics would include more practical high tech ideas such as
spherical trigonometry and three dimensional vector analysis, useful
since we do not live on a plane surface.

If you are just beginning, prepare for a somewhat long ride. Formal
instruction will cut the time involved.

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