trigonometry - Trigonometry If you took a course in...

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Trigonometry If you took a course in trigonometry, and spent hours on the many esoteric minutiae that it can lead to, I want to assure you that the number of those concepts that you use in day-to-day work is small. But, you use those every day: The definitions of the sine, cosine, and tangent. A few of the identities among them. Mostly, how to recognize them in unfamiliar contexts. The basis of trigonometry lies in the fact that for similar triangles, the ratio of cor- responding sides is the same. Remember that similar triangles have the same shape (not necessarily the same size), so that their angles are equal. The trigonometric names are simply the titles given to these ratios in the particular case of a right triangle. a' c b θ a b' c' The definitions are sin( θ ) = a c = a 0 c 0 , cos( θ ) = b c = b 0 c 0 , tan( θ ) = a b = a 0 b 0 . The Greek letter θ (theta) is commonly used for angles, as is the Greek letter φ (phi). The other definitions, such as the cotangent: cot θ = 1 / tan θ show up too, but less often. From the definitions, you immediately get an identity: tan θ = a b = a/c b/c = sin θ cos θ . Similarly, start from the Pythagorean theorem, a 2 + b 2 = c 2 , and divide both sides by c 2 : a 2 + b 2 = c 2 = a 2 c 2 + b 2 c 2 = 1 , or sin
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This note was uploaded on 01/08/2012 for the course PHYSICS 205 taught by Professor Galeazzi during the Fall '11 term at University of Miami.

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trigonometry - Trigonometry If you took a course in...

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