Some of the trigonometric identities used in prosthaphaeresis, an early method for rapid computation of products, were named " Werner formulas " in honor of Werner's role in development of the algorithm.
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:As for 60?and 135?and so on, these can be related back to other facts using the identities listed at Trigonometric identities # Periodicity, symmetry, and shifts; the rules can be justified visually.
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Substituting ( 10 ) and ( 11 ) in ( 8 ) and ( 9 ) and simplifying using trigonometric identities results in a sum of constant terms, sine and cosine, at angular frequency 2 \ omega.
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The result was "'WP : SNOW "': delete and userify to User : Daviddaved / A trigonometric identity for a circulant matrix . c ) 06 : 06, 2 March 2010 ( UTC)
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To perform the huge number of multiplications needed to produce much of his astronomical data, Tycho relied heavily on the then new technique of " prosthaphaeresis ", an algorithm for approximating products based on trigonometric identities that predated logarithms.
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We now use the Pythagorean theorem, the fact that the slope of the curve is equal to the tangent of its angle, and some trigonometric identities to obtain " ds " in terms of " dx ":
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:Perhaps the questioners want to say that many of the identities given at Trigonometry and List of trigonometric identities are presented without any justification as to why they should hold .-- Lambiam 16 : 05, 11 October 2007 ( UTC)
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:where the trigonometric identity \ sin ^ 2 x = \ frac { 1-\ cos 2x } { 2 } has been used and the factor \ sqrt { 2 } is called the crest factor, which varies for different waveforms.
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A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the None of these solutions is reducible to a real algebraic expression, as they use intermediate complex numbers under the cube roots.
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I guess cos ( 30?) = sqrt ( 3 ) / 2 is useful too; you can get it from the sine with the Pythagorean trigonometric identity . 90?should also be automatic, as well as 0? just visualize them to figure out where the 0s and 1s go.
