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There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.
The quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = (″) and the above approximation follows when tan X is replaced by X.
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin( α + β ) = sin α cos β + cos α sin ...
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
Seventy-seven Nobel laureates are urging the Senate to vote down Donald Trump's nomination of Robert F. Kennedy Jr. to run the nation’s top health agency, ...
A former Tennessee teacher who got pregnant after raping a 12-year-old boy pleaded guilty and has been sentenced to 25 years in prison with no parole. On Dec. 20, Alissa McCommon, 39, of Covington ...
From January 2008 to December 2012, if you bought shares in companies when Bonnie G. Hill joined the board, and sold them when she left, you would have a 128.0 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
O.J. Simpson prosecutor Marcia Clark revives the forgotten 1950s murder trial of Barbara "Bloody Babs" Graham and discusses decades of evolving true crime coverage.