To: Teacher2Teacher Public Discussion
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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