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Unformatted text preview: r 2 (which we can do since r > 0) gives r 2 r 2 = x 2 + y 2 r 2 = x 2 r 2 + y 2 r 2 = p x r P 2 + p y r P 2 . Since r 2 r 2 = 1, x r = cos , and y r = sin , we can rewrite this as: cos 2 + sin 2 = 1 (3.3) You can think of this as sort of a trigonometric variant of the Pythagorean Theorem. Note that we use the notation sin 2 to mean (sin ) 2 , likewise for cosine and the other trigonometric functions. We will use the same notation for other powers besides 2. From the above identity we can derive more identities. For example: sin 2 = 1 cos 2 (3.4) cos 2 = 1 sin 2 (3.5) from which we get (after taking square roots): sin = r 1 cos 2 (3.6) cos = r 1 sin 2 (3.7)...
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 Fall '11
 Dr.Cheun
 Calculus

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