Just wondering why they have separate courses since trigonometry is geometry?
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That's a good question, one I have wondered about too. I've never had a course called "trigonometry," but I've had high school geometry and analytic geometry (pretty much pre-calc), college calculus and advanced calculus, and graduate real and complex analysis.
The first few paragraphs of http://en.wikipedia.org/wiki/Trigonometr… help explain it.
Trig is a branch of geometry. I think that it focuses somewhat more on an analytic approach to geometry, and gets deeper into trig functions. The usual geometry course doesn't put the geometric figures into a coordinate system (x-y plane, or 3-space) but just works with angles and line lengths of free-standing figures. Trig, like analytic geometry (not sure how to describe the difference between them), exploits the power of using algebra and a coordinate system.
E.g., proving that some pair of lines in a figure are equal may be rather complicated using "synthetic" (Euclidean) geometry techniques. But put coordinates onto the points, and you can solve for the exact coordinates, and show that the lines are equal. The algebra involved in an analytic proof may also be somewhat complicated, but doesn't require all the complicated steps that the a synthetic proof does.
So trig is sort of an advanced approach to geometry taking much from algebra and Euclidean geometry and blending them together. At least that's my impression.
I'm not sure I've given you a very good answer, but these are my impressions of where trig stands in the spectrum of mathematics.
The first few paragraphs of http://en.wikipedia.org/wiki/Trigonometr… help explain it.
Trig is a branch of geometry. I think that it focuses somewhat more on an analytic approach to geometry, and gets deeper into trig functions. The usual geometry course doesn't put the geometric figures into a coordinate system (x-y plane, or 3-space) but just works with angles and line lengths of free-standing figures. Trig, like analytic geometry (not sure how to describe the difference between them), exploits the power of using algebra and a coordinate system.
E.g., proving that some pair of lines in a figure are equal may be rather complicated using "synthetic" (Euclidean) geometry techniques. But put coordinates onto the points, and you can solve for the exact coordinates, and show that the lines are equal. The algebra involved in an analytic proof may also be somewhat complicated, but doesn't require all the complicated steps that the a synthetic proof does.
So trig is sort of an advanced approach to geometry taking much from algebra and Euclidean geometry and blending them together. At least that's my impression.
I'm not sure I've given you a very good answer, but these are my impressions of where trig stands in the spectrum of mathematics.
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Trig is not just geometry. It can be applied to measuring energy as well.