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 θ , and y r = sin θ , we can rewrite this as: cos 2 θ + sin 2 θ = 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 θ to mean (sin θ ) 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 θ = 1 − cos 2 θ (3.4) cos 2 θ = 1 − sin 2 θ (3.5) from which we get (after taking square roots): sin θ = ± r 1 − cos 2 θ (3.6) cos θ = ± r 1 − sin 2 θ (3.7)...
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus

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